The pdf of a continuous RV X is given by f(x) = cos(Ax)+ 10, where x E [0, -1. Find the value 2A of A + 0.

Q: Find the derivative, dy/dx: y = x² In x3 ý =- 2 1-4 ln x x³ In? x 3. ý = -2 In x – 2x | y = --(- 3…

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Q: Let f(x) = | 1°dt. Evaluate the following. f'(x) = f'(-6) =

A: ∫xn dx   xn+1 /n+1 + C f(x) = ∫x0 t6 dt       = [t7/7]x0   f(x) = x7/7

Q: Show that

A: ∫x f(x) dx=x F(x)-G(x)                                  F'(x)=f(x)G'(x)=F(x)

Q: f(x)=210, where is it continuous?

A: Given: fx=210 We know that graph of given function is horizontal line for every value of x

Q: Find the derivative: eY sin(x) = sec(xy) – 5 dy dx

A: Some formulae that you will use: Product rule of differentiation:           other formulae:

Q: Find the derivative of the function. 2x F(x) = arctan(t) dt Vx F'(x) : %D

A: The given problem is to find the derivative of the given definite integral function. We have to use…

Q: Find the second derivative of F(t) = | sin(x) cos(2)d.r.

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Q: 4x Let F be the function defined by F(x) = cos(t?) dt. Find an expression for 3. F'(x).

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Q: Let f(x) = (x² + 3x)e*. Determine the value of the third derivative of f(x) for x = 0.

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Q: Let f(x) = cos(3/7). Find f'(x). f'(z) =

A: Recall: df(g(x))dx=f'(g(x)).g'(x) dcos xdx=-sinx dxndx=nxn-1

Q: d sec(11x – 4) dx = dt 13

A:

Q: 9a) Find the local extrema of the function f(x) = e*(x² -3) using the Second Derivative Test.

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: