12. So · u(x) = 1 = x - √ ª (x − t)u(t)di 0

Q: Consider the function f (x) = 6x² + 4x + 2. Find F(x) so that F' (x) = f(x). %3|

A: f(x)=6x2+4x+2To find: F(x) such that F'(x)=f(x)

Q: 12. Consider the equation x = ( 1 ) x x' -5 -3 Express the general solution in terms of real valued…

A: The given system of differential equation is:x'=1-51-3 x

Q: Suppose that f(x + h) – f(x) = 5hx + 8h – 6h². Find f'(x). f'(x) =

A: Given: fx+h-fx=5hx+8h-6h2, To find: f'x.

Q: 8. Find f'(x) for the function f (x) = (5x² + 3)4

A: ddxfxn=nfxn-1f'x

Q: f(x) = 3x² - 2cos(x) find the equation for f'(x).

A: Consider the fucntion

Q: 6. If g(x) = x'+x²+ g"(2). find the value of

A: see 2nd step.

Q: Find the GS for x³y"" + 6x²y" + 4xy' — 4y = 1 − x − 2x² -

A: Solution:-

Q: 57. Verify that S2 yields the exact value of | (x – x³) dx.

A:

Q: Q1. f(ath) - fla) = - 1hac? +2hu-3hza+Ih2+5 h3 %3D Find f'(x)

A: To find f'(X)

Q: 1. f (x² + 1)(x² + 3x) dx

A: To evaluate the given integral.∫x2+1x3+3x4dx

Q: Consider the function f(x) = 3x² + 30x + 83 Determine an expression for the derivative of f(x).

A: f(x)=3x2+30x+83

Q: dy 5. x- 3y = x². dx

A: (5)We need to find the solution of given differential equations

Q: Find the d. c. of T from definition.

A:

Q: 3- 2 -3 2 -1 2 3 g(x) = sinh(x) -1 -2

A: the symmetry used here is the y-axis which divides the graph into 2 equal portions.  the graph given…

Q: 7. 1 x lnx dx 8. f(x + 1)(2x - 1) dx

A: 7.∫1x lnxdx = ∫1 lnx. 1xdxLet, lnx= y ⇒1xdx = dySubstitute the corresponding values in the…

Q: 20) S(tanh (4– 3x) kdx

A:

Q: O X 3. Find f'(x) when f(x) = √16x²

A:

Q: 1. Find the function f(x) if f'(x) = 3x² – 2.x +5 and f(0) = 5 %3D

A: Given, f'x=3x2-2x+5f0=5 To find, The function f(x).

Q: Seven thieves try to share a hoard of gold bars equally between themselves. Unfortunately, six bars…

A: Seven thieves try to share a hoard of gold bars equally between themselves.Unfortunately, six bars…

Q: 54. If h(x) = √√/4 + 3ƒ(x), where ƒ(1) = 7 and ƒ'(1) = 4, find hʼ(1).

A: If , then to find .

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

A:

Q: 22. Find the "natural" domain of the function f(x)=16r +Vx. x'-16x

A:

Q: 9. [f(x)dx -1

A: Find the integral from the given graph

Q: 4. x(x² – 1)² dx

A: Solution:

Q: 6. FinD F(S) if f(t)= t· cost

A:

Q: 1. Find f(x) if f'(x) = x/x and f(1) = 2

A: Given that: f'(x)=xx and f(1)=2

Q: x) such that f"(x)=2r' +3x-4

A: Integration: f''(x)=2x3+3x2-4x+5; f0=2, f1=0 ∫xndx=xn+1n+1+c

Q: 10. f(3x - 1)(x - 1) dx

A: The given integral is:∫-113x-1x-1dx

Q: 7.If f(x)= 2x – 1 and g(x)= x² – 2x, find f(3)/g(2). -

A: Given fx=2x-1 and gx=x2-2x. To find: f3g2 Solution: Finding f3.  f3=2·3-1=6-1=5 Now, finding g2.…

Q: =- Determine the values of c and d for f(x) = fƒ (7) = 0. For what value(s) of x is f(x) increasing?…

A:

Q: Let f(x) = X x - a Find the value of a so that f'(1) = 1 - 4

A: This question is based on Quotient rule of differentiation.