1 dx is divergent True O False

Q: Evaluate the integral.

A:

Q: Evaluate 1cos ax dx and 1sin ax dx, where a is a constant.

A: We know that, ∫cosθdθ=sinθ+C           ⋯⋯1∫sinθdθ=-cosθ+C     ⋯⋯2 (a) We have, I=∫cosaxdx Let us…

Q: 1-) dx dx n above is separable.

A:

Q: Set dx dy where

A: We have to solve given problem:

Q: dy Find given 3xy = In x. %3D dx

A:

Q: Find

A:

Q: sp dy dx dz (1–z) Evaluate .

A:

Q: Find dy/dx at the given point. 3x' + 4xy = 1 at (-1, –1) O a. 4/5 O b. 5/4 Ос. 1 O d. -5

A: Using  differentiation of product rule,

Q: Show for Re(z) > 1 dx = r(2) ((2). et - 1

A:

Q: -1 dy find dx If y = %3D (1-VE)

A:

Q: Use an appropriate technique to evaluate the following: 1 dx dy (1+ x² + y²)²

A:

Q: dy is let y = (sin æ)*an 7 then dx

A: Given

Q: Find d2x/dt? as a function of x if d 6x sin x. dt? ||

A:

Q: dy olution of the DE =CO dx 2x + C nx + C (x) + C

A: We have to choose the correct answer from the given options according to the given information

Q: Find dy if y = (1 – æ*) * dx

A: The function is given by y =1-x314 To evaluate : The expression

Q: 2.f(t) = cosh wt sin wt

A:

Q: xe* dx Jo (1+x)

A: Given                                            I=∫01xex1+x2dx now,…

Q: If y = In(x² + 5) + sinx function then ay at x = 0 is ? dx 11 10 1 10 O 1 O 5

A: Given, y=lnx2+5+sinx  We have to find  dydx at  x =0

Q: Find dx/dt: x = 2[cos (t/2)]^2

A: x=2cost22

Q: Use this information to evaluate 1 (1- e)| dx %3D x=1 et - 1

A:

Q: FIND DY/DX OF THE FOLLOWING 6. y=sec'Inx

A:

Q: . In (3xy) %3D х+ x5

A:

Q: determine dy/dx if xy = ecsch(x)+picos(0)

A: The given implicit equation is: xy=ecsch(x)+picos(0) Clearly cos(0) = 1, so…

Q: determine dy/dx if xy = ecsch(x)+πcos(0)

A: Given, xy = ecsch(x)+πcos(0)

Q: dy Find dx if y In(x2 32)

A: Given:

Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: (2) /: (2) 5te dt (1) dx 5+e*

A:

Q: Evaluate S. So dy 0 dx √√[y(1+x²)]

A: Problem is solved using concept of integral.

Q: dy In(5a + 2) Find for y = %3D dx

A: Giveny=ln(5x+2)7e5xdifferentiate…

Q: 3 2 Find for y = dt, where x> 9t+2 dx dx

A: The given function is y=∫0x39t+2dt. Let u=9t+2. Then, du=9 dt. The upper limit will be 9x+2 and the…

Q: -6, find dy dx Given that y = ln

A:

Q: If y = V1-x² sinx, prove that (1–x²) +xy =1– x². dx

A: Given that :- y=1-x2sin-1x Prove that :- 1-x2dydx+xy=1-x2

Q: Find So S 4:xy dx dy.

A: Evaluate the integral.

Q: 7. Calculate dy/dx at the point indicated: f(0) = (7tan O, cos O), 0=/4

A: Here we will use the concept of parametric equation and Derivative of parametric ewyations

Q: 1 dx is finite -1 X Select one: True False

A: True

Q: dx 5 + 4 sin a

A:

Q: Find de when y = In(1+ 5/æ) dx

A: The objective is to find derivative.

Q: Find dy/dx: (a). y = cos 8x + sin r2, (b). y = Vcos 8x + sin x². %3D

A:

Q: 2.f (t) = cosh wt sin wt

A:

Q: dy Find if y = In|9 + x|. dx

A:

Q: 1. Use residues to evaluate 1 : xe dx , (a>0).

A: Let fz=ze-zz2+a2 The poles of the function fz are ±ai Choose the contour C consisting of the real…

Q: 7) Find dx if y- J

A:

Q: Use an appropriate technique to evaluate the following: 1 dx dy (1+x² + y²)²

A:

Q: (1) So“ dx let t=x o Vx

A:

Q: If y = √1 − x² sin¯¹x, prove that (1− x²) ¹ + xy = 1− x². dx

A: We can prove the given the result by differentiating the given function.

Q: d'y Use implicit differentiation to find if 2.x2 – 3y? = 5. dx? - dy %3D dx? ||

A:

Q: 37. Use Fubini's Theorem to evaluate dx dy. 1 + xy

A:

Q: find ds/dt. s = sin t/1 - cos t

A: Given    S=sin t1-cos twe have to find dsdt

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.