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: (1) So E 00 e-x dx let t=x

A: We evaluate given integral using gamma function

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: 6. Disks of polycarbonate plastic from a supplier are analyzed are analyzed for scratch resistance…

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Q: 5) Find if y = (cos h x)* dx

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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: | Cas (41 - ) dt (a) (b) Cos* () Sin () 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(x), where f'(x) = sin(x) + cos(x) + 1 and f(#)=2. %3D %3D

A: Using anti derivative formula.

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: 3. If f(x) X-x find F(tanx) 1+x2

A: 7.The given limit is: limx→-∞x23x2-4x+1 To evaluate the value of the limit.

Q: S* (1– x)e* dx

A: To find out the integration.

Q: 3. Integrate the function. (a) / Vx–1dx = %3D (b) /e2+ 2x+1 dx = (c) | (sin xcosx+ sinx cos x) dx =…

A: Hello there! You seem to have uploaded a question with multiple subparts. As per our guidelines, we…

Q: dy Find if y = log5u, where u = cos5x %3D dx dy = - 5tan5x dx dy = 5tan5x dx dy = -tan5x dx None

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Q: dy dx if e*y = sin-1y+ x²y + Find

A: Given exy2=sin-1y+xy2+yπ

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

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: e probability of A is 0.60, the      probability of B is 0.45 ,and the probability of both is 0.30.…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: f(x) = 2 sin x + 8 cos x, then f'(a): f'(x) = f'(5) = |

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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: Find given that y=[atan-¹(bx)]². dy dx Assume a,b ER. 2[atan-¹(bx)] O 2[atan-¹(bx)]- O 2b[asec²(bx)]…

A: To find dydx given that y=a tan-1bx2.Assume a, b∈ℝ

Q: e 9. cos(x) dx - " sin(x) dx. Evoluate

A: Formula:∫ cos x dx = sin x + C∫ sin x dx = - cos x + C

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(z) : f'(z) =D %3D coS I - 6 tan z, then %3D

A: NOTE: Refresh your page if you can't see any equations. . take derivative

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)