Show that Show that Show that fexx dx converges for any p = R. In xdx and f′ (x(ln x)(1 + x²)−¹)dx converge. x-P cos xdx converges for p > 0 and converges absolutely if p > 1.

Q: Show that for some number a > 1, we have 1- <= In(a) <= a – 1. Hint: In(a) = S"dx, please check the…

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Q: Let ƒ(x) = (x³ + 4x + 6) ³ f'(x) = 9x¹ + 12x² f'(1) = 2541 X OF

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Q: d (d) Use the Inverse Function Theorem to prove dr = -/n-1 for all I E (0, 00), n E N.

A: Here we have to prove that ddxx1n=1nx1n-1 for all x∈(0,∞),n∈N by using inverse function theorem.

Q: By using the substitution u = x3", ir

A: Given, by using the substitution u=x3n, then   To find:   (1).   ∫nx3n-1ex3nex3n+8dx   (2).…

Q: Let n be a positive integer. Prove that 1:(1)+2 (;) . (:)- n n + 2 . +n . n2"-1. ... n

A: We have to prove the identity: 1·n1+2·n2+....+n·nn=n2n-1

Q: 3. For a, b>0 define f(x) by f(x) = Tot tz ta dt log blog a Prove or disprove that f is continuous…

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Q: Let fn(x) = 1+cos2 2023 (na). Does {f} converge uniformly to a function f on R? √n

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Q: Show that X. dt f(x) J3 V1 + t4 is one-to-one. f'(x) = Since f'(x) O for all x, f is increasing v on…

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Q: Let ƒ(x) = ln(−5x² + 3x + 10) ƒ'(x) =

A: use logarithmic differentiation

Q: Explain the conditional expenditure function in equation (1). Express this equation in a traditional…

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Q: Let f(t) = 4t* – 4t + 5e'. Then f'(t) =

A: find the derivative

Q: Compute the exact probability (using integral calculus) that the lecture continues for at least 60…

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Q: Suppose that f is an integrable function on R (real numbers).  How do you show that the integral  of…

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Q: d dx f(x) = ex, f(0) = 8.

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Q: Use mathematical induction to prove that the n-th derivative of (x +n + 1)e" is given by d" (x+1)e =…

A: We use mathematical induction. The detailed solution is typesetted and given in detailed as the next…

Q: Let R be the rate at which customers are served in a queue. Suppose that R is exponential with pdf…

A: Given: Let R be the rate at which customers are served in the queue. The pdf of R is given as:…

Q: Suppose that f : [a,b] → R is continuous and with continuous derivative f'. Suppose also that f(a) =…

A: Suppose f:[a,b]→R be a continuous and continuously differentiable such that f(a)=f(b)=0 and…

Q: Let 7(t) = Find 7'(t) 7 (t) =

A: Topic - vectors and derivatives Since r→t = 5 t5-1, -e-t, -3 sin2t we to find r→'t  derivative of tn…

Q: Consider the following linear programming problem: Max Z= 15 x₁ + 16 x2 s.t. 20 x₁ + 10 x₂ s 60 X₁ +…

A: We have to find the lower bound of the x2 coefficient.

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

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Q: Let 6х — 8 - f(x) = ln 5x + 4 f' (x) =

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Q: Use Newton's method to find the absolute maximum value of the function f(x) = 2x cos(x), 0 ≤x≤x,…

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Q: Use a comparison test to determine whether I (ln(x) — 1) dx converges or diverges.

A: (i) If f(x)≤g(x),∀x∈[a,∞) and ∫a∞g(x)dx is convergent,  then ∫a∞f(x)dx is convergent. (ii) If…

Q: Let f(x) = 7x° In(x) + 3 5 f'(x) =

A: We have to find

Q: 7. Find the intervals of increasing/decreasing for the function f(x) = x'e*

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