5. If F(x) = a. F'(1) b. F(2), by interpreting F(2) as an area √4t-t² dt, evaluate the following:

Q: Find f. f"'(t)  = t   - √t

A: To find f"(t) we integrate f"'(t)

Q: 3x + 5x #2. R(x)= 일 때 R'(0)을 %3D 1+3x° + 6x° + 9x°

A:

Q: If f(2)=9 and f'(2)=2, estimate f(1.9).

A:

Q: find Zrr and Zss for function Z(r,s)=ln(2r+3s)

A: Given that  find Zrr and Zss for function Z(r,s)=ln(2r+3s)find Zrr and Zss for function…

Q: Estimate f (2.1) if f (2) = 1 and f'(2) = 3.

A: Given: The linear approximation of f at a is one way of writing the equation of the tangent line at…

Q: Differentiate. 7t f(t) t3 - t - 1 f'(t) =

A:

Q: . If f(x) = V4x – 7, find f'(x).

A: we have ;  f(x)=4x-7;  we have to find f-1(x)

Q: 2x Find F'(x) given F(x) = S t2dt. -2x

A:

Q: Q/ Use Lagrangian polynomial to find f'(2.1) from the following table 1 2 3 f(x)| 10 17 22

A: Numbers of data point set is 3, so the degree of polynomial will be at most degree 2.

Q: 2. Determine the exact value of f'(2) for f(x) = (2e³ + 3e-6x)5.4,

A:

Q: Differentiate the function. H'(z) = H(z) = In c²-2² c²+z²

A: H(z)=lnc2-z2c2+z2

Q: If a = 1 − v^2 and both x and v are zero when t = 0, show that x = −1/2ln(1-v^2) and hence find v^2…

A:

Q: Differentiate the function. R(a) = (6a + 1)² R'(a) = 12 X

A:

Q: Q6. Verify that 8²1 əxəy for the function f(x,y) = ln(2x + 3y)

A: Given,            fx,y=ln2x+3yTo find : Verify that ∂f∂x∂y for the given function.

Q: calculate the value of coth-1(x) when x is greater than 1

A:

Q: Find f. 13 f"(x)=x³+ sinhx, f(0) = 4, ƒ(2)= 5

A:

Q: P=S/(S+F) Express S in terms of F and P

A: A function defines a relationship between two sets, where one set is dependent on other set. Any…

Q: Find f. f"(t)  = 3/√ t  ,f(4)  =20, f'(4)   =7

A: We have to find f where, f''t=3t, f4=20 and f'4=7. Integrating both sides, ∫f''t…

Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

Q: (b) Evaluate In(x) dx 1

A: The given integral is divergent.

Q: Let F be the function given by F (x) = S" (sec² (5t) – 1) dt. Which of the following is an…

A: We have given that   F(x) = ∫2x(sec2(5t)-1)dt        ...(1). And we have to find F'(x). To find the…

Q: Differentiate the function. •¹ (33) H(z) In =

A: H(z)=ln⁡(a2−z2a2+z2)

Q: 11 2. Find a formula for the inverse of the function and verify that evaluating df/dx at x-a and…

A:

Q: compute ref(i) when f(z)=sqrt(z-1) and f(0)=-i

A: Given:It is given that  and .To Find:We have to compute .

Q: 6. Differentiate the f(x) = 2x 12x а. e 4 1 b. 4 С. еx d. e2x

A: Given: fx=12e2x Now differentiate the given function we get, dfdx=ddx12e2x=12ddxe2x…