Ге-). 5x) dx х Je t(4t2 - 1)3 dt

Q: d. sinh - u = 1 du dx V1 + u? dx

A: To find the derivative

Q: dy satisfies dx? 2 iven by

A:

Q: ( sinh u) = du =(cosh u) dx dx dx A) True B) False

A: We need to tell whether the given statement ddx(sinh u)=ddx(cosh u)dudx is true or not.

Q: Set dx dy where

A: We have to solve given problem:

Q: dy If dx = COS s 2x, then what is y?

A: The derivative is given by dydx = cos2x                         ........(1)

Q: F ind So S. eu dy dx.

A: Use the concept of reversing the order of integration. While integrating with respect to one…

Q: -을 x e [T, 3 J Sinx =

A:

Q: sp dy dx dz (1–z) Evaluate .

A:

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

A:

Q: dt || y whent = 0, y =

A: Please refer to the image below

Q: If f = 5x2y2 - XY2 then find af at (3,1) %3D dx

A:

Q: 2 sin(t) s(t) = et

A: Part (a) The displacement of the object is, s(t)=2sintet Integrate the expression with respect to t…

Q: sin(2t + ) dt = 00 64e 4. O O OG

A: Here in this problem we have to find ∫0∞sin(2t+π2)e2t-3dt

Q: Evaluate | (3t + t²) sin(2t) dt

A:

Q: dy is : If x- y 0, then %3D dx

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: cos ax -dx = re¯ª,a>0. .2

A: With the help of Residue we can prove given result:

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

A:

Q: - 16y? – 16x – 16y = 0. dy at the point (3, dx ves to calculate

A:

Q: Show for Re(z) > 1 -dx r(2) ((2). 1 er 0.

A:

Q: Solve the D. E J+gtanx = sin ex

A:

Q: dy 3) Determine the of : In (ху?) %3D х у dx

A:

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

A: Given:

Q: Find ds/dt if 3t + 3s sin(3t) + 3cos(t) %3D

A:

Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

A:

Q: 1. Use a substitution to find (6a2 + 2)e*+# dx showing working.

A:

Q: (cos) dydx 2πT O Option 1 Option 2 1 EIN 2

A: We need to evaluate double integral. Let , I = ∫π2π ∫0x2 1x cosyx dydx To find double integral first…

Q: S Si dydx %3D 1-r

A: To evaluate the given double integral.

Q: find dy/dx and dy/dx2, if : x = a(cosθ + θsinθ) and  y = a(sinθ - θcosθ)

A:

Q: 125. y = / V2 + cos³t dt

A:

Q: Evaluate tan x (t² cos 4t-3) dt dx Jo

A:

Q: -31 cosh 2t 7. (a) 2e- sinh 3t (b)-

A:

Q: etany) dy cos?(y)

A:

Q: 3. Stanh3x dx = Jsinh3x, Ssinh3x_ dx %3D u = cosh3x du = %3D

A:

Q: tan (e) 1+z* (d) (22+ cosh 2z)dz () z coshz dz zp-

A:

Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 6, and dz/dt = 6.  (Enter your answers as a…

A: We would differentiate the given expression implicitly w.r.t. t, ........................(1)

Q: 8 cos (2r² + 2y²) dy dr Hint You could take a cab to the pole.

A: Given the integral is ∫02∫04-x28cos2x2+2y2dydx

Q: -dnd auf for the feaoy) =tan Cx+y). 3xし y

A:

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

A:

Q: d (cos² 2x)=-2sin 4.x dx 12 Show that %3D

A:

Q: a) Prave that sinlx t Cos-lx = ½ %3D

A: To prove,   sin-1x+cos-1x=π2

Q: Find the value of zr» at the point (0, 3, 2) where a²y² + 2² – cos(ryz) = 10.

A:

Q: 7) Find dx if y- J

A:

Q: 3e7" sin(2y) 3e7 sin(2y) dy

A:

Q: Integrate both sides = S sec²y dy = S dx

A: ∫sec2y dy=∫dx

Q: dx dy If L = Va? + y?, = -5, and dt = 2, find dt dL when a = 3 and y = 7. dt %3D dL dt

A: Given query is the derivative of L over t at x = 3 and y = 7.

Q: Cos Vt dt 3. Evaluate

A: The integration of the given integral is; Cos√t/√t.

Q: S 6 ttan t dt = %3D dx Jx

A:

Q: dy -2y 3cos3t – 11sin3t dt? dt

A: