Q1: You roll a die 5 times. What is the probability that at least one value is observed more than once? T T 3T Q2: Let Rx = {0, 4' 2 %3D 4 such that, Px(0) = Px()= Px() = Px() = Px(#) = !! %3D find E[sin(X)].

Q: Let f(x) = cos (x). %3D If it is true that f" (x) = x(f'(x))ª for some constant a, find the value of…

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Q: Given f''(x) = – 9 sin(3x) and f'(0) = – 4 and f(0) = 5. %3D %D Find f() =

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Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

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Q: Evaluate each of the following: (a) /" In(x) dx

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Q: Find f. f"(0) = sin(0) + cos(60), f(0) = 3, f'(0) = 1 f(0) = %3D

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Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: dy dx if e*y = sin-1y+ x²y + Find

A: Given exy2=sin-1y+xy2+yπ

Q: 7. Find (a). pln e" sec? e" dx (b). 2V5x3+4 dx

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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: f(z) = cos(4r +5) %3D

A: we have to derivative  we know that  d(cos (ax+b) ) = -sin (ax+b) a                        = - a sin…

Q: Let y = g(x) cos (In x). Compute y'(1), if g(1) = 1 and g'(1) = -2.

A: We have to find the derivative of y at x=1

Q: If f(x) = csc(3x). then f' (x) = %3D o -3csc(3x)cot(3x) o -3csc2 (3x) o 3sec(3x)tan(3x) o 3tan? (3x)

A: Given: fx=csc3x To evaluate: f'(x)