Q:1. Evaluate Cosny dy Q:2. Prove that 16 X (1+x) dx 306

Q: Solve the following Exact DE using Method of Grouping. 2) (y sec?x + sec x tan x)dx + (tan x + 2y)dy…

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Q: Indicate whether the following statement is true or false. siont e dy dx = fSi P(cos(0)? dr d0 False…

A: Double Integrals conversation to polar coordinates

Q: Prove that when y = e 2 Sin 2.x, then 4- d y dy +17y=0 +4. dx? dx

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Q: d (arccot(x)) -1 Be sure to provide a written justification for 5. Prove your work. dx 1+ x2

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Q: Find fr(x, y) and fy(x, y) given f(x, y) = tan x· cos os(x² – y?).

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Q: Q:Ifx = sin 6, y = 0,y= cos p6, prove that (1-x )y, xy,+ p°y= 0, dy and y1 d dy where y, %3! %3! de

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Q: Exercise: Answer the following by finding dy/dx. 5sin-1 # – cosh x (a) y = Vsec4 x + In 7 4 (b) + In…

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Q: d Q 3. Prove that tanx dx sec?x. =

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Q: 52. If z = f (x, y), where x = r cos 0 and y = r sin 0, find a. Əz/Ər, b. дz/80, and c. d z/Ər d0.

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Q: O Evalmate the impaper mitegral on e Show that it DE VERGES dx x In? (x) 2. tan (x) dx

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Q: e Suppose flx) = Sin (x) For which value %3D of a, osas T, will f'la) = 0.

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Q: Given f(x,y) = ex cos y, Evaluate f,(0,2) (A) -sin 2 B) 0 C) e² D cos 2

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Q: Use the attached equation to find  dy/dx for this: 5tan−1(x2y) = x + xy2

A: Given, 5tan−1(x2y) = x + xy2

Q: - If x=sect and y = tan t, evaluate at t of the following: 4. dy (a) dx d y (b) dx?

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Q: Given that 3x - tan y = 4, what is dy in terms of y? A 3sin y

A: I have provided solution in step2

Q: dy at t = dx? Let x = 3 cos t, y = 4 sin t. Find 4

A: Derivative Question

Q: where yco,t) = y (5,t) = = 2Jx2 and y cx, o) y (X,o) = 10 sin 4T X

A: We solve the differential equation by the method of saperation of variable. In this method we…

Q: dy Find ax for the following function. y = x cos x sin x dy dx

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Q: If x= sect and y= tant, evaluate at t = of the following: 4 dy (a) dx (b) d’y dx

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Q: 2. for, (x+y)X = tan-14x + TT* + dx dy a)- Find InIny

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Q: iven that y = sin? (t) and x = cos ( 4t?), hence find dx dy a. 8t sin (8t) sin 2t 8t sin ( 8t2 ) b.…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: None of the choices…

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Q: Let f(x)= sin(x) – e¯*, po=0, and p,=1, then by Secant method p2=

A: f(x) = sin(x) -e-x  p0 = 0 and p1= 1

Q: Use at least 6 decimal places of accuracy 1. C sin (z² + 2) dx using n = 6 2. √ √² +6dz √² +6 dz…

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Q: Q3 Suppose that w = x² + y² + z² x = e" cos 0 ,y= e"sin0 ,z = re® aw аnd ar aw Find дө

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Q: For dv: choose something w It is not always possible to fo EX-1- Evaluate the following in 1) [xe*…

A: We are entitled to answer three sub-parts. Please resubmit the question which you wish to get…

Q: Find dy dx? A) y = 3sin u - sin'u and x 3 cos u- cos'u

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: that y?=x+ sin Cxy) - T 2 and let ß Be the value of dy evalwated atlxy

A: Given- y2=x2+sinxy-π24 To Find- The value of dydx at π2,1 and considering that value as β and then…

Q: The approximation of I = , tanx dx using composite Simpson's rule with n-5 is: None of the choices O…

A: f(x) = tanx Each interval h=(b-a)/n =1-0/5=1/5 =0.2 xO=0, x1 =1/5, x2=2/5, x3=3/5,x4=4/5, x5=1…

Q: d 1 (cot-'x) : dx Prove that 1+x?"

A: Let y=cot-1x. Then coty=x.

Q: Given f(x, y) = 3x* cos (y), find COS fzy(x, y) = fyw (#, y) = | %3D

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Q: Given f(x,y) = ex cos y, Evaluate fx(2,0) A cos 2 B) sin 2 C) 0 D) e²

A: fx is the partial derivative w.r.t. x

Q: Given that r = 3 cos nt, y = 3 sin at and z 4nt with 0<t <1. Evaluate (x+ 2) ds.

A: The line integral is defined as,

Q: Using the substitution x = 2 cos 0, what is the value of f, V4-x2dx. (b) *1+2vx dx using u = 1+2Vx…

A: a) It is required to find the value of ∫124-x2dx using substitution x=2cosθ. Differentiate x=2cosθ…

Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) Oe2 0 0 O cos 2 O-sin 2

A: The given function is: fx,y=excosy   As we know that; The common derivative; ddxcosx=-sinx And…

Q: Explain the relation between the following two formulas ( c is aconstant):

A: Consider the provided formulas, ddxsincx=ccoscx   and   ∂∂xsinxy=ycosxy Explain the relation between…

Q: Show all steps to verify that fry = fyx given f(x, y) = cos(2x) – x²e5y + 3y²

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Q: Show that given R: x € [0,1] ^ y € [0,2] 1133 3x²yexy dy dx = 6 R

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Q: Given f(x) = , 1+ cos²(t) t? - 9 dt %3D 0. At what value of x does the local max of f(x) occur?

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Q: Exercise: Answer the following by finding dy/dx. 5sin-lr cosh x (a) y = Vsect x + In 7 4 (b) + In y…

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Q: given y = ƒ(u) and u = g(x), find dy/dx =dy/dx = ƒ'(g(x))g'(x). y = sin u, u = x - cos x

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Q: 1. Given xy = sin x , show that d'y 2 dy +=+y = 0. dxx dx

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Q: Given f(x,y) = ex cos y, Evaluate fx(0,2) O e² 00 O cos 2 O-sin 2 M

A: We have to find the derivative

Q: Given z= f(x, y) is differentiable and x= e' sint and y = e' cos t ôz a) Show that + + ду ôs b) Find…

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Q: A certain substitution gives S sin*x)cos"(x)dx = S (u²-u*)du .what is n?

A: For substitution- Balancing the above equation, we can solve it as follows-

Q: If the substitution U = Jx is used, then S dx is equi valent to ?

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Q: 6. If x= sect and y=tant, evaluate at t =- of the following: dy (a) dx d'y (b) dx?

A: x = sect y = tant

Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) A cos 2 B) e² CO (D) -sin 2

A: This question can be solved using the concept of partial derivatives.

Q: (2n (c) t³ sin (t²) dx

A: Topic:- integration

Q: x sect and y= tant, evaluate at t = - of the follow 4 dy (b) d y dx?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.