2

local/tmp/image-0001...3. Either integrate by parts or use Fubini's theorem: r—l x P(X > x) dx r f (y) dy clx r—l rx dx dy — yr f (y) dy. An alternative proof is as follows

Download PDF Report

Upload
others
View
0
Download
0

Embed Size (px)

Citation preview

Page 1: local/tmp/image-0001...3. Either integrate by parts or use Fubini's theorem: r—l x P(X > x) dx r f (y) dy clx r—l rx dx dy — yr f (y) dy. An alternative proof is as follows

Page 2: local/tmp/image-0001...3. Either integrate by parts or use Fubini's theorem: r—l x P(X > x) dx r f (y) dy clx r—l rx dx dy — yr f (y) dy. An alternative proof is as follows

eduwavepool.unizwa.edu.om€¦ · Use dy/dx = I/(dx/dy). (y — 2r)ez = 2 — y + 21, dx/dÿ = —2 + ÿ — 21 is linear, dx/dÿ + 2x = — 2, x = + y/2 — 5/4 u = c, uxdx + uydy

eduwavepool.unizwa.edu.om€¦ · Use dy/dx = I/(dx/dy). (y — 2r)ez = 2 — y + 21, dx/dÿ = —2 + ÿ — 21 is linear, dx/dÿ + 2x = — 2, x = + y/2 — 5/4 u = c, uxdx + uydy

Documents

HIGHLIGHTS - jkshahclasses.com - … · 8 10. y = (9x3 1). tan x Differentiating wrt x ; dy = (9x3 1). d tan x + tan x d (9x3 1) dx dx dx = (9x3 1) . sec2 x + tan x . 27x2 = (9x3

HIGHLIGHTS - jkshahclasses.com - … · 8 10. y = (9x3 1). tan x Differentiating wrt x ; dy = (9x3 1). d tan x + tan x d (9x3 1) dx dx dx = (9x3 1) . sec2 x + tan x . 27x2 = (9x3

Documents

· Exercise 5.3 2x + 3y = sin x Differentiating both sides with respect to x, we get — sin x dx dx dx dy cosx — 2 dx 2x + = sin y dy dx cos x Question 2: 2x + = sin y Answer

· Exercise 5.3 2x + 3y = sin x Differentiating both sides with respect to x, we get — sin x dx dx dx dy cosx — 2 dx 2x + = sin y dy dx cos x Question 2: 2x + = sin y Answer

Documents

C4 Edexcel Solution Bank - Chapter 4...4 dx dt dy dt dy dx 4 sint cost dx dt dy dt dy dx sec2 t sec t tant sec t tant 1 cost cost sint 1 sint dx dt dy dt dy dx 2 sin2t 2 − 2 cos2t

C4 Edexcel Solution Bank - Chapter 4...4 dx dt dy dt dy dx 4 sint cost dx dt dy dt dy dx sec2 t sec t tant sec t tant 1 cost cost sint 1 sint dx dt dy dt dy dx 2 sin2t 2 − 2 cos2t

Documents

dx x - University of Colorado Boulder · PDF file · 2014-12-22... nd dy=dx. (a) y= 3x3 + 2x2 p x Answer: dy dx = 15 2 ... Find the value of the integral: R 7 0 f0(x)dx Answer: R

dx x - University of Colorado Boulder · PDF file · 2014-12-22... nd dy=dx. (a) y= 3x3 + 2x2 p x Answer: dy dx = 15 2 ... Find the value of the integral: R 7 0 f0(x)dx Answer: R

Documents

Extension 1 Mathematics 3U - Sydney...d) Find dy if y = e 2x cos-1 x dx e) Find dy at t = ::. if x = 2 cos t and y = 2 sin t dx 4 2x f) Solve - ~ x + 4 x-3 g) Use the substitution

Extension 1 Mathematics 3U - Sydney...d) Find dy if y = e 2x cos-1 x dx e) Find dy at t = ::. if x = 2 cos t and y = 2 sin t dx 4 2x f) Solve - ~ x + 4 x-3 g) Use the substitution

Documents

MA 108 - Ordinary Differential Equationsdey/diffeqn_autumn13/lecture6.pdf · If r(x) 0 in the equation d2y dx2 + p(x) dy dx + q(x)y = r(x); that is, d2y dx2 + p(x) dy dx + q(x)y =

MA 108 - Ordinary Differential Equationsdey/diffeqn_autumn13/lecture6.pdf · If r(x) 0 in the equation d2y dx2 + p(x) dy dx + q(x)y = r(x); that is, d2y dx2 + p(x) dy dx + q(x)y =

Documents

Deformation: Displacement & Strain...x xx y yy u dx dx A B AB ux AB dx x v dy dy A C AC vy AC dy y HH HH ·w ¨¸ cc w©¹w w ·w ¨¸ cc w©¹w w •Normal strain; xy 2 vu CAB xy

Deformation: Displacement & Strain...x xx y yy u dx dx A B AB ux AB dx x v dy dy A C AC vy AC dy y HH HH ·w ¨¸ cc w©¹w w ·w ¨¸ cc w©¹w w •Normal strain; xy 2 vu CAB xy

Documents

Lesson 8 - justcalculus · 2016. 12. 23. · Summary: The Flow of A Vector Field ALONG a Closed Curve: R C ³ ³³m(x,y)dx n(x,y)dy rotField(x,y)dx dy Let C be a closed curve parameterized

Lesson 8 - justcalculus · 2016. 12. 23. · Summary: The Flow of A Vector Field ALONG a Closed Curve: R C ³ ³³m(x,y)dx n(x,y)dy rotField(x,y)dx dy Let C be a closed curve parameterized

Documents

Computer Graphics 7 - Rasterisation · Testing for the side of a line I Assumethelineisbetween(x l,y l) and(x r,y r) I Theslopeofthelinewillbe dy dx wheredx = x r −x l and dy =

Computer Graphics 7 - Rasterisation · Testing for the side of a line I Assumethelineisbetween(x l,y l) and(x r,y r) I Theslopeofthelinewillbe dy dx wheredx = x r −x l and dy =

Documents

An integral lift of contact homology - Columbia Universitymath.columbia.edu/~nelson/2017_penn.pdf · d = dy ^dx = dx ^dy) ^d = dx ^dy ^dz Jo Nelson An integral lift of contact homology

An integral lift of contact homology - Columbia Universitymath.columbia.edu/~nelson/2017_penn.pdf · d = dy ^dx = dx ^dy) ^d = dx ^dy ^dz Jo Nelson An integral lift of contact homology

Documents

· Question 11: xx2-3 + (x — 3) x2 for x > 3. Answer 11: and v = (x — 3)x2 therefore, y = Letu = Differentiating with respect to x, we have dy du dv dx dx dx x2-3 taking log

· Question 11: xx2-3 + (x — 3) x2 for x > 3. Answer 11: and v = (x — 3)x2 therefore, y = Letu = Differentiating with respect to x, we have dy du dv dx dx dx x2-3 taking log

Documents

156 Section 4.1 Chapter 4 () More Derivatives solns.pdf · dy dy du dx du dx = 62 6 6 662 (cos ) ( ) (sin)() sin sin ( ) dd ux du dx u u x =+ =− =− =− + (b) dy dy du dx du dx

156 Section 4.1 Chapter 4 () More Derivatives solns.pdf · dy dy du dx du dx = 62 6 6 662 (cos ) ( ) (sin)() sin sin ( ) dd ux du dx u u x =+ =− =− =− + (b) dy dy du dx du dx

Documents

11.differential equations final - Sakshieducation.com ...sakshieducation.com/EAMCET/mathematics/Bitbanks/Calculus/... · 2 2 3 / 2 2 / 1 d y dx dx dy ... 1 −x 2 dx −1 −y2 dy

11.differential equations final - Sakshieducation.com ...sakshieducation.com/EAMCET/mathematics/Bitbanks/Calculus/... · 2 2 3 / 2 2 / 1 d y dx dx dy ... 1 −x 2 dx −1 −y2 dy

Documents

Core Mathematics 3 Differentiation - KUMAR'S MATHS ...C3 differentiation Page 6 By chain rule dy dy du dx du dx cosx 12u = 12cos x sin x = 6 sin 2x u u So finally: d (6sin x sec2x)

Core Mathematics 3 Differentiation - KUMAR'S MATHS ...C3 differentiation Page 6 By chain rule dy dy du dx du dx cosx 12u = 12cos x sin x = 6 sin 2x u u So finally: d (6sin x sec2x)

Documents

Potential Energy Length hence dl-dx = (1/2) (dy/dx) 2 dx dU = (1/2) F (dy/dx) 2 dx potential energy of element dx y(x,t)= y m sin( kx- t) dy/dx= y m

Potential Energy Length hence dl-dx = (1/2) (dy/dx) 2 dx dU = (1/2) F (dy/dx) 2 dx potential energy of element dx y(x,t)= y m sin( kx- t) dy/dx= y m

Documents

Calculus Differentiation dy/dx = y y = e x e ix = cosx + i sinx

Calculus Differentiation dy/dx = y y = e x e ix = cosx + i sinx

Documents

156 Section 4.1 Chapter 4 () More Derivativesdy dy du dx du dx = 62 6 6 662 (cos ) ( ) (sin)() sin sin ( ) dd ux du dx u u x =+ =− =− =− + (b) t dy dy du dx du dx = ππ 231

156 Section 4.1 Chapter 4 () More Derivativesdy dy du dx du dx = 62 6 6 662 (cos ) ( ) (sin)() sin sin ( ) dd ux du dx u u x =+ =− =− =− + (b) t dy dy du dx du dx = ππ 231

Documents

Uplift Education / Overview · Web view2012. 10. 3. · 2. derivative: d 2 y d 2 x = d dx dy dx = d dθ dy dx dθ dx = d dθ dy dx dx dθ = 1 dx dθ d dθ dr dθ sin θ + rcos θ

Uplift Education / Overview · Web view2012. 10. 3. · 2. derivative: d 2 y d 2 x = d dx dy dx = d dθ dy dx dθ dx = d dθ dy dx dx dθ = 1 dx dθ d dθ dr dθ sin θ + rcos θ

Documents

TRANSFORMS AND PARTIAL DIFFERENTIAL …...11. Find the general solution of px+qy=z Answer: The auxiliary equation is dx dy dz x y z From dx dy xy Integrating we get log x = log y +

TRANSFORMS AND PARTIAL DIFFERENTIAL …...11. Find the general solution of px+qy=z Answer: The auxiliary equation is dx dy dz x y z From dx dy xy Integrating we get log x = log y +

Documents

& Conducted I - CH - 11... · 6 01. y = x . tan x Differentiating wrt x ; SUMS ON PRODUCT RULE dy = x d tan x + tan x . d x dx dx dx

& Conducted I - CH - 11... · 6 01. y = x . tan x Differentiating wrt x ; SUMS ON PRODUCT RULE dy = x d tan x + tan x . d x dx dx dx

Documents

MATHEMATICS...23. The integrating factor of the differential equation y 2log x dx dy xlogx is given by (A) ex (B) log x (C) log (log x) (D) x Ans : (B) Hints : x y dx x x dy 2. log

MATHEMATICS...23. The integrating factor of the differential equation y 2log x dx dy xlogx is given by (A) ex (B) log x (C) log (log x) (D) x Ans : (B) Hints : x y dx x x dy 2. log

Documents

SLOPE FIELDS ASSIGNMENT #15 NAME 1. - WordPress.comSLOPE FIELDS ASSIGNMENT #15 NAME_____ 32 6. 1 dy x dx =+ 7. 2 dy y dx = 8. dy y dx x = − 9. At right is a slope field for the differential

SLOPE FIELDS ASSIGNMENT #15 NAME 1. - WordPress.comSLOPE FIELDS ASSIGNMENT #15 NAME_____ 32 6. 1 dy x dx =+ 7. 2 dy y dx = 8. dy y dx x = − 9. At right is a slope field for the differential

Documents

Differential Equationsdx dy + 2 =-ans: y=e-x+ce-2x 2. 2 sin 3 x x y dx dy x + = ans: x3y=c-cosx 3. xdy + ydx = ydy ans: y y c x = + 2 4- Exact The equation M(x, y)dx + N(x, y)dy =

Differential Equationsdx dy + 2 =-ans: y=e-x+ce-2x 2. 2 sin 3 x x y dx dy x + = ans: x3y=c-cosx 3. xdy + ydx = ydy ans: y y c x = + 2 4- Exact The equation M(x, y)dx + N(x, y)dy =

Documents

Solved Examples - MasterJEE Classes...Example 5: The solution of the differential equation x 2 2 dy dx = 1, given that y = 1, dy dx = 0, when x = 1, is Sol: By integrating x 2 2 dy

Solved Examples - MasterJEE Classes...Example 5: The solution of the differential equation x 2 2 dy dx = 1, given that y = 1, dy dx = 0, when x = 1, is Sol: By integrating x 2 2 dy

Documents

HAPTER 5: Derivatives of Exponential and Trigonometric ...msmamath.weebly.com/.../6/...ch_5_nelson_solutions.pdf · dy dx 5 d(xe3x) dx 56x2ex3 dy dx 52(3x2)ex3 y 52ex3 dy dx 5 1 2!x

HAPTER 5: Derivatives of Exponential and Trigonometric ...msmamath.weebly.com/.../6/...ch_5_nelson_solutions.pdf · dy dx 5 d(xe3x) dx 56x2ex3 dy dx 52(3x2)ex3 y 52ex3 dy dx 5 1 2!x

Documents

10. 11. · 2016-01-15 · dy e t dx dx ee e dt − = − = dy =dt = = 0.005 5. 6. 7. A 22 2 2 3 dy t = 3 2 3 3t thus dx t22 2t t4 d d d y dt =; 3 t dt dt dx dx dx dt ⎛⎞dy ⎛⎞dy

10. 11. · 2016-01-15 · dy e t dx dx ee e dt − = − = dy =dt = = 0.005 5. 6. 7. A 22 2 2 3 dy t = 3 2 3 3t thus dx t22 2t t4 d d d y dt =; 3 t dt dt dx dx dx dt ⎛⎞dy ⎛⎞dy

Documents

CALCULUS · y = 2 when x — 1 when x — 3C, - —9C1 sin3x — 9C2 cos 31 ... the points given in the table. 2 4 14 o 4 o 4 6 dy/dx — X COS dy/dx o 4 4 o 209 . ... Consider Example

CALCULUS · y = 2 when x — 1 when x — 3C, - —9C1 sin3x — 9C2 cos 31 ... the points given in the table. 2 4 14 o 4 o 4 6 dy/dx — X COS dy/dx o 4 4 o 209 . ... Consider Example

Documents

Differential Geometry Jay Havaldar v[x] = dx dx v1 + dx dy v2 + dx dz v3 = v1 Intermsofthegradient: dx= v[x] = (1;0;0) v= v1 In other words, the differentialdxis a function which sends

Differential Geometry Jay Havaldar v[x] = dx dx v1 + dx dy v2 + dx dz v3 = v1 Intermsofthegradient: dx= v[x] = (1;0;0) v= v1 In other words, the differentialdxis a function which sends

Documents

FIRST ORDER DIFFERENTIAL EQUATIONSassets.openstudy.com/updates/attachments/501902dfe... · FIRST ORDER DIFFERENTIAL EQUATIONS 3 3 (x2 y2)dx+(2xy)dy= 0 dy dx = y2 x2 2xy dy dx = y

FIRST ORDER DIFFERENTIAL EQUATIONSassets.openstudy.com/updates/attachments/501902dfe... · FIRST ORDER DIFFERENTIAL EQUATIONS 3 3 (x2 y2)dx+(2xy)dy= 0 dy dx = y2 x2 2xy dy dx = y

Documents