Question 10 („P)P dx Suppose a E R, where a>0, a ± 1 What is A a*- In(a) B xa* -1. In(a) ха* a D xa*-1

Q: This is an example from the text. Can you show me how to get the slope? I do not fully understand…

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Q: Question 19 Let F(x) -1. √1+t¹ dt for x in (-∞0, ∞o). Find F'(- 5 sin z O F'(x) = -√1 + cos²x O…

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Q: Question 11 puas √1+1² Ffxx)=f -dt, then f'(x) equals 0 I+e' In(secx)√1+tan²x Itela tanx sec³x 1+ele…

A: Topic:- application of integration  Note :- as per our guideline if more than one question uploaded…

Q: Question 1 π 2x Evaluate the integral cos(xy)dydx 4

A: ∫45∫0π2xcosxydydx

Q: a+b log (a cos 0+6° sin 8) de log a>0, b>0. 2

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Q: Question 2 [17] 2.1 If f(x;y) = sin(xy) +x* In y, find f., at (0:4). 2.2 Let f(x; y) = arctan y 2+x?…

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Q: 3 1. Determine the order and the degree: sin x () - e* () = xy dx². a. Order – 2; Degree – 3 b.…

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Q: QUESTION 2 16х + 7 Solving the integral /. dx yields: бх2+х— 12 )3 In(2x+3) + –In(3x – 4) +c a.…

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Q: Ax) = Ln=0 n! e Show that: GAx)dx = En=1 n(n+1) (–2)"-1 (n +2)! ||

A: Here we use integration and series theorems to find the solution.

Q: a) sin2021 (2mr)dr re gln z b) Ip- c) | In(csc r) cot rdr 1 d) 2r – a2 et - e- dr ez +e- e) 을 In 3…

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Q: Question 2 > The function ` f(x) = (5 x-9)e^(-6 x) ` has one critical number. Algebrically use the…

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Q: 31. (a) 32. (a) 33. (a) 12x-1| dx √2 + x) dx e* - 1| dx L'i lex -3π/4 (b) cos x dx (b) [*/² | } −…

A: Given: ∫-11ex-1dx

Q: Chapter 23 | Implicit Differentiation and Chain Rule 1. Find dw/dt given w = 5 cos(xy) – sin xz, x =…

A: Here the given equation is w=5cosxy-sinxz, x=1t, y=t, z=t3.

Q: Question 16 In (ale) (2-sec2x)emlesec'x sec( 3A – x) What should be the value of A for dx to be…

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Q: QUESTION 5 Suppose that g(3,4) - 2, g,(3,4) = 6, and g,(3,4) = 3. What is the value of the…

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Q: Question 9 19. Se3z tanh(e3) In cosh(e³²)dz a. 1/6 (In cosh (e"))² +c c. 1/3 (In cosh (e))² +c b.…

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Q: Question 2 d cos x Find dx In x A. X sin x x In x sin x+cos x x (In x) 1 COs X x In x sin x+cos x D.…

A: To find differentiation  ddxcosxlnx

Q: Question 4. Show that the average value of f(x) ei. = e- + cos x on the interval [-7/2,0] is

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Q: Question 10 of 17 > dh\ dt =2 5 The variable h is the height of the ladder's top at time t, and x is…

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Q: Question 2) Solve the initial value problem having the initial conditions. (Hint: Each time,…

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Q: Question 3 If f(x) = f A sec ³x 1+elanx B 1+tan²x 1+etanx In (secx) √ 1+tan²x C tanx 1 + e sec²x D…

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Q: QUESTION 3 a) Evaluate the integral tanh (2x)sech (2x)dx.

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Q: QUESTION 5 The approximation of x e*dx by Simpson's Rule is 0.160602 O 0.160603 O 0.162402 O None of…

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Q: Question 5. Evaluate the indefinite integral 2020 (x) tan 2021 (x) dx. COS“

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Q: e 2*(1 – e *x)- J (arcsin e 2x) cos2 (In arcsin e2x)

A: Given,           ∫e2x1-e4x-12arcsine2xcos2lnarcsine2xdx

Q: Question 6 (: The indefinite integral 2+1 dx equals (a) [1/x²] In(x2 + 1) (b) [1/x]In(x² + 1) ()…

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Q: Question (1) Find the Following Integ (1) S(x? 1 +3) dx (2) S

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 1 cos 3x dr b) VAr + 7 (In z)3 dr xe²? dx d) ſ e™ sin(e") dx e) f) sin x tan x dx (Hint: tan x = cos…

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Q: 8. Using any work found in Question 7, determine the 3x (x? - 5)° dx a.

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Q: Question 3. Let a € (0,1) and define f : T→R by 1 f(x) = sin(nx) na n=1 for all r E (-T, 7]. Prove…

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Q: QUESTION 2 Determine a potential function for F(x,y,z) = sin(y)e³²i - xsin(y)e?j + 3xcos(y)e32k or…

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Q: Question 3 2 approximate '(x – 5)" dx using Riemann sum, the partition of 4 subintervals To X - each…

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Q: Question 5 Does x2 – 10 = x x sin x have a real solution? Show your process. %3D

A: yes the equation have real solution

Q: QUESTION 4 witQUTMOUTMOU with respect to r. Differentiate y 3- cosh r 6+ sinhr MO

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Q: 3 Question 5 Example 6.4.2 of APEX Calculus uses this fact (which appears in an integral table): f…

A: The objective is to find the right option.

Q: Question 4 Evaluate sin (Inx) dx- Integration by parts will be used repeatedly. What is the…

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Q: Question 001: Complete the following question involving Substitution Method. Given the integral 2x +…

A: Given:∫e2x+7dx

Q: 1. x(0.2)° – 20.6 = 10 [cos () sin (E) + sin (E) cos () cot + sin ) cos () cot 2. log,(x + 12) = 2…

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Q: Problem 11 Evaluate the indefinite integral.  ∫sec^3(x)dx=____________ +C

A: Given integral can be written as Integrating by parts, we get

Q: QUESTION 5 10 If continuous and Jx)dx = 54, then which one of the following numbers can take at…

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Q: Example 1 Find dy/dx, if a. y=sin(x² + 3x + 1) b. y = cos² (2x-1)

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Q: 10. r(0) = log,(nsin® – sin" 0)

A: The question is taken from the calculus and the subtopic is derivative of the function so we have to…

Q: a十o log (a cos 6+6 sin 6) do=w log a>0, b>0.

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Q: Question 170 Calculate f 3 in x.cos x dx. (a) 3sin x cos x , In 3 (b) 3cosx . In 3 (c) 3sin x. In 3…

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Q: Question 11 Integrate f 9z2 - 5+dz Type only the numeric value below and be sure to show all of your…

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Q: Question 10 tanx If f(x)= A (B) C D sec ³x Itelin sec²x Iteline 1+1² I+e' -dt, then f'(x) equals…

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Q: Example 1 Differentiate each of (a) f (x) =2 x' cosh x sinh t (b) h(t)=

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Q: Question 6 Given: f (x, y, z) = cos(xyz) + ln x5 - sinh y² + 3z Find: af(x, y, z) дz at P(-1, 3, 0)…

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Q: Activity 6: Find the first and the second derivative of the following: 1. у 3D е cos x 2. y = sin³…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…