c2 0 < x< a, 0

Q: Q₂ / let then find X Y f(-2) 9 S f(x) dx 3 17 2 -> 1 5 10 f (11) f (3.2), f" (3.2) 5 -3 7 9 f funda…

A: As per guidelines,we are supposed to solve first 3 subparts only.I have given 4.

Q: Let f(x) = 2x e¯x*,x > 0 and Let Y x2. Find G(y)and g(y). %3D

A: In this question,  we need to transform the variable in the probability density function.

Q: = f(x) g(x) If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = y 6…

A: The given graph of the functions is shown as,Let,Note:  As mentioned in the instruction, we are…

Q: Find the derivative of F(x) = f (t³ - t) ³ dt. O 5 (t³-t) (3t²-1) ○ (x³ - x) 5 ○ 5 (2³-x) 4 O 3t² -…

A:

Q: [2x*dx (Ans. 3 2 x' +c ); (xi) J3x°dx - 3 In\x)| 3 |3x'dx (Ans. (Se* –x? +2)dx , (x + 0) (x) x' +c);…

A:

Q: 3 tanx dx 3/ secx

A: Indefinite integral: An integral which does not have any upper limit or lower limit of integration…

Q: TLP iadade mnts & smt Findf F'(t) =sec(t) (seclE)+ tan (ED), -st < f- FCt) = -<ts f (--7 2.

A: We simplify f'(t) by expanding  To find f(t) we integrate f'(t) C=integrating constant

Q: = = √²* (t²³ + 5t² + 4) dt 0 If f(x)= then f''(x) =

A:

Q: Find the 3rd derivative of the function y (2z-8z2 +3) (z+3) O y"=120z2 192z + 42 120, 198z + 72 =…

A: We need to find the 3rd derivative of y=2x3-8x2+3x2+3 . So,      y'=2x3-8x2+3x2+3'…

Q: Let h = fog where ƒ : R² → R and g: R² R² is defined by g(x, y) = (3x²y, x – 2y). Find the…

A: Letandfind the derivative

Q: 10) Suppose F(x) = | (1² – t)dt for all real values of x, then F'(4) = %3D (A) 12

A:

Q: The derivative of a function F (X, Y) at a point P_0 = (1,2) in the direction towards P_1 = (2,3) is…

A: Given That : The derivative of a function F (X, Y) at a point P_0 = (1,2) in the direction towards…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 16) y = (x2 - 2x + 1) eX B) (x2…

A:

Q: Find the partial derivative dz for the function z = cos(x³ +y²).

A:

Q: Q2// A) Derivative following functions by using chain rule m 1) y = Vu, 2) y = 4u, -Va+1 Vx+1

A:

Q: Find f if f"(t) = 2e¹ + 3 sin(t), f(0) = −4, ƒ(ñ) = 9. f(t) = 2e^t-3sint-6

A:

Q: The line y=x-1 is the tangent line to the a) f(x)= -cosh²x at the point (o, f(o)) the tangent line…

A:

Q: Let f (x) 6x + 3 Then the derivative of f is 2х— 1 Ax + B f'(x) where (2x – 1)C' %3D B = C = || ||…

A:

Q: The graph of f'(x) is shown below. Give the interval(s) where the graph of f(x) is concave up. y =f…

A:

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x (x+ 3)5 15) у - In 6х- 8 A)…

A: Given that:y=ln1-xx+35To find derivative

Q: 8(x) 48. f(x) 2 - x' In Exercises 51–60, show that f(g(x)) = x an dom x - 1 g(x) of 51,fx) = 2r + 1,…

A:

Q: dy 2²+1 Use the quotient rule to find the derivative of the function y = dx О А. dy 1 = 2x(x+ V) –…

A:

Q: Find the x and y coordinates on the graph of f (x) = x³ - 3x where the tangent is horizontal. (A)…

A:

Q: F'(x) = (ax3 + b)2 O none of the choices O 1 За ах3 + b 1 1 2a ax3 + b 1 1 - За аx3 + b. o 1 2a (…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.