3. Solve for fe)(r) given that f(r)% = sinh(3r)

Q: 1 I = J dx (1-x²)Z %3D 3

A: It is known that: 1-cos2x=sin2x∫sec2x=tan x+Ctansin-1x=x1-x212

Q: f(x)% 3D tanh In(2x) is equivalent to

A:

Q: 5. Change of variable 2 x dx 3x+1 a.

A: Given function, ∫12x3x+1dx

Q: nd for z = ln(2x - y).

A: Given query is to find the derivative.

Q: S(3 – x) dx 12

A:

Q: dx 2(x - 2)²

A: To evaluate,∫1x2x-22dx

Q: Prove the following equation : Cosh(3 x) = 4 cosh³(x) – 3cosh(x)

A:

Q: If a= 1/x + 1/y, what is the value of 1/a?

A:

Q: f fo=2x and g)= x-4. what is the value of rCg(3))?

A: f(x)=2x and g(x)=x-4

Q: The number of books in a library increases at a rate according to the function B'(t) = 360 e the…

A: Given : The number of books in a library increases at a rate according to the function…

Q: (a) Define what it means by for y = f(x). %3D

A: In this question we have to define the meaning of dydx for y=fx

Q: a. (x² – 4x – 4)(y² + 1)dx + 2y(x³ – 2x² + 4x – 8)dy = 0;

A: a. Given,                (x2-4x-4)(y2+1)dx+2y(x3-2x2+4x-8)dy=0    and     x=4, y=1.

Q: Evaluate J dx √x(1+√x)

A: ∫1udu = lnu +C

Q: (b) Find the differential for y = -5 %3D

A: Giveny=4x-53   ...(1)

Q: 3-2n 2. Suppose ak is an infinite series with partial sums Sn %3D 2+n k=1 etermine the value of lim…

A: We have find limit

Q: If f(x) = x , then find the value %3D of f'(a). write solution in excct form.

A: We can make it easier for you

Q: 10) The function A how to find how long it will take for the bacteria to reach a total of 5000.…

A: The function 503t represents the amount of bacteria A present in a petri dish after t hours.

Q: 1/4 S (2 + sec)? dx

A: Please go through the attached solution. I hope that it  will help you .Thankyou . Best regards.

Q: cosh x dx е e- 2х

A: Given integral is ∫coshxe-2xdx

Q: 3 Solve S (x dx.

A:

Q: A toy manufacturer determined that the total cost in dollars of producing a slime kits in one day is…

A: We have given total cost in dollars of producing x slime kits in one day is given by…

Q: 39. g(t) = t coth /t² + 1 %3D

A: We have to find the derivative

Q: x/y.x/y÷y/x= 18.26/27

A: Given expression, xy·xy÷yx=18·2627

Q: 1. Solve for 'x': vx + v2x +7 = 8

A:

Q: If f(x) = 16, find f'(7).

A: Please refer the attached image for complete solution.

Q: (i) Hz+t is constant for 0 < t < 1 and (ii) qz = 0.16. Calculate the value of t for which ¿P, =…

A: We are given that the force of mortality is constant for any one year and the remaining information…