4.1 Suppose that fig and g'are continuous on the interval 1= {x :asxs b). Show that a ) exists, and furthermore show that | (z)dg(a) = | (")/(x)dxr.

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A: c) Given density is, fx=0.375x2, 0≤x≤2 Consider, P30 sec≤X≤90 sec=P0.5 min≤X≤1.5 min)     since, 1…

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A: Uniformly Continuous:-  Here we prove the result using a theorem of uniformly continuous.

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Q: 4. Suppose fand f'are differentiable functions of x. Given f' (4) = 0, f" (-), and g(x) = (). log…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Q11 Determine all the critical points for the following- S(x) = sin'x- cosx On the interval (0, 2n).

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Q: 9. 6) Suppose that g is continuous and that g(x) dx = 2 and g(x) dx = 16. Find g(x) dx.

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Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

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Q: 4 Suppose that f(1) 3, f(4) = 5, f '(1) = 4, f '(4) = 2, and f " is continuous. Find the value of xf…

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Q: 4 Suppose that f(1) = 9, f(4) = -7, f'(1) = 6, f'(4) = -1, and f" is continuous. Find the value of…

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Q: 2. Suppose the PDF of X is given by fx(x) = 5e-5x(o)(x). Find its CDF.

A: Solution

Q: If 0 < f(x) < g(x) for all x and I f(x)dx diverges, then | g(x)dx diverges. 13 Select one: True…

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Q: 1+ By using the definition In(1+x) = / 1 -dt, show that for a certain range of values of r, t…

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Q: 4. Find the maximum value of f (x) = In(x – In x) on the interval -sse. e

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Q: 4. Find the first two intervals using the bisection method to compute the minimum of the function…

A: We need to find the first two intervals of on the interval

Q: Find an upper bound for the Lagrange interpolation error for f(x) sinh(x)+2 cosh(x) over the…

A: Given: fx=sinhx+2coshx, x∈0,2. Interpolation nodes xk=k4, k=0,1,⋯,8. To find:          An upper…

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Q: , 6]. che function on this interval. 1/sqrtx ow there exists a c in the open interval (2, 6) such tl

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Q: 3. Consider the function g(x) defined by | 22 sin(1/x) if x > 0, g(x) = –x² if x < 0. (a) Show that…

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Q: 3. Use the IVT to prove that y = x ln x has at least one zero on 2'2

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Q: 2.4 Use the definition of the derivative of complex function to show that f(z) is not dif-…

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A: The Lorenz curve  of country X is f(x)=12x2+12x4. The GINI index  of a certain country with Lorenz…

Q: If f(x) = SEs rlog3 x 3t %3D dt and is differentiable on an interval, which cotx csc2t of the ff. is…

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Q: Suppose that f (x) has a continuous derivative, сп/2 f(-1/2) = 0, f(T/2) = 1/4 and f (x) dx = 3.…

A: The method of substitution is a very significant method in evaluating definite integral. The…

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A: Given: limn→∞ 2n∑k=1ncos1+2kn To convert this into the integral , use the following method

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Q: 1. Evaluate the definite integral S ,2 C (9x² + 5)dx by the limit definition.

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Q: If g(g(x)) is continous at 0, then g(x) is continous at 0.  True or False?

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Q: 1, fund warginal cictribution for h(x) for 2. Fud condhtimal pdf4 t) . Estaati yi/ a) V. Estuate…

A: As per the guideline, 3 subparts can be answered. please repost the remaining subpart. thank you.

Q: y²

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Q: 5. Consider the function S 2r – 1, si x < 2 f(x) = 6-x, si x 2 2. The Limit x 2 f(x) is:

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Q: 4 '2 If f is continuous and f(x) dx = 10, find | F(2x) dx. %3D

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Q: 1. Suppose that g(x) > 0 for all r, g(x) has a continuous derivative, g(-2) = 5 8 g(4) = 3 and |…

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Q: Which of the following graphs is the slope field for dx 12 -3-211. s 2 13 US 111-2-/35 1112 111²-111…

A: Here we have to solve the given differential equation and plot the solution

Q: 5. Show that |Logz|<|In(z)|+ t, for all z # 0.

A: