Given a continuous function of which is twice differentiable, if f" (c) > 0, which of the following is true? f is concave upward at x = c Of is concave downward at x = c Of has a relative minimum at x = c f has a relative maximum at x = c

Q: Find the area of the given region using any method. y 1 49 - x² y

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Q: a) [₁ 3]: Evaluate the integral 3x - 1 (x + 4)(2x - 1) / dx.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: integral of sin^6 y cos^6 y dy

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Q: 2 84 +81 √ s(3² +9)²0 ds

A: 2. Given Integral,∫s4 + 81ss2 + 92 ds

Q: If 2 cos 2t = 1/5 then sin² t = Select one: O True O False 13 30

A: We can find the answer as below.

Q: Find the equation of the tangent line to the curve x²y² - xy + x - y = 0 at the point (0, 0). Ox+y=1…

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Q: If x = f(u) and v= g(x), what is du dr dx du ○ f'(u)g'(x) ○ f'(u) + g(x) O dv dx + dx du dv du by…

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Q: f (x-2)(x+1)' dx

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Q: Let y= 3x2 +7x+4. If Δx=0.4 at x=2, use linear approximation to estimate ΔyΔy

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Q: Suppose f'(x) = x² - 1. Then the graph of f is concave upward on 0 (-∞0,0) O (-1,1) (0,00) O (-∞,…

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Q: Evaluate (i) dx S √e xlnx√(2lnx)² – 1

A: We are asked to evaluate the integral

Q: Starting from the same point, Angela starts walking eastward at 6 m/min while Jessica starts running…

A: Please see the below picture for detailed solution.

Q: 3. Arctany dy

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Q: If f is a differentiable function and such that and g(x) = x+2 / 1+f(x) such that f(0) = -2 and…

A: We have to find the the value of g'(0).

Q: A right circular cylindrical container with volume 167 cm³ is to be made. Use the method of Lagrange…

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Q: A B O A OB O OD 1 13 (sin(3z))¹⁰ + C 1 33 ſ cos(3z)sin¹⁰(3z) dz 1 3 (cos (3z))¹¹ + C F None of the…

A: Here we have to find the integral.

Q: x+3y=x².

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Q: r(t) = (−2 cos (2t), 3 sin (3t), In (2t)), then the fr(t)dt is equal to 3 Cos cos 4 where C is a…

A: Given:    rt=-2cos2t,3sin3t,ln2t then  ∫rt dt =∫-2cos2t,3sin3t,ln2tdt…

Q: Evaluate fcot (x) cos²x dx

A: The given integral: ∫cotxcos2x dx.We need to evaluate the above integral.

Q: ind f. f ″(x) = −2 + 24x − 12x2,    f(0) = 2,    f ′(0) = 18

A: We can solve the given equation.

Q: Condense the expression to the logarithm of a single quantity. 3 log3(x) +log3(y) - 8 log3(z) X

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Q: Evaluate f dac x²-x+2

A: We can evaluate the integral as below.

Q: For the curve f(x) = Find the horizontal and vertical asymptotes. x-4x² +2 x² - 4x +4

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Q: Jo 1 X dx =

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Q: Bob, Trinity, and Roger are painting their living room. Trinity takes twice the number of hours that…

A: This question can be solved using the concept of time and work.

Q: Evaluate: lim 8118 x6x² + x²-1 8x6 + 4x³ + 10

A: see below the calculation and answer

Q: Evaluate the definite integral by the limit definition. L₁x³dx

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Q: Two cars start moving from the same point. One travels south at 60mi/h and the other travels west at…

A: We have to find distance between two car

Q: Determine the indefinite integral below. S(9x+4)²dx. (9x+4)²dx =

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Q: For the piecewise defined function None of these 2 what should be the value of c so that we have…

A: In this question we have to find the value of c so that f(x) is left continuous at x=1

Q: A B O A OB D 1 4 1 4 f sec² (4t) (3 tan(4t))³ dt 1 16 (3 tan (4t))+ + C (3 - tan (4t))+ + C E None…

A: This question can be solved using the concept of integration by substitution.

Q: If u = (0, 2, 3) and v = (1, 3, -1), find the projection of u onto v. 이름다 a) Obl 이유ㅎ ○ c) (1, 1, -1)…

A: This question can be solved using the concept of vector projection of a vector on other vector.

Q: Solve: x²y + xy' -n²y = 0 General Solution: y = C₁ *letters only a.x2n b. x-n a.xn b. x-2n c. x2n…

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Q: Find the centroid of the region bounded by the graphs of the equations using any method. y = √9-x²,…

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Q: Solve the given dy=x√ e+~

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Q: Question 1 described by the vector function r(t) = (4t² ln t, t-4 29 -2e-³t). a) Find the integral…

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Q: Question 2 [ Given the function xye* f(x, y) = 2x³ +50y² a) Find the domain of f. b) Find exist. lim…

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Q: d dx 0.8 - - 3.4x^2 +6x)

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Q: f '(t) = 10 cos(t) + sec2(t),    −?(pi)/2 < t < ?(pi)/2,    f(pi/3) = 4 find f

A: Taking anti-derivative,

Q: Find the derivative of the vector function, r(t) =

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Q: 4. fx(2x - 1)'dx

A: This is a problem related to integration. Please find the general procedure given below. As per the…

Q: E A4 sin (e-² + ln z) + C 4 sin (-e-²) + C B O A § 4 (½ − e¯²) cos (e¯² + Inz) dz B E None of the…

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Q: 3. (x² + y²)dx - 2xydy = 0 [Answer: x²-y² = cx]

A: Here we use the method of substitution y=vx then dydx=v+xdvdxsee below the calculation and…

Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: Use implicit differentiation to find dy given y³2 – log(x²y¹) = cos¯¹(1). dx

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Q: Use an appropriate test to determine whether the series converges. 1 2 3 24³ 25 By the + + + Limit…

A: here, we will use comparison test to check the convergence .

Q: Fill in the blank to complete the trigonometric identity. so(-u)- sec = X

A: This question is based on Trigonometric identity.

Q: ax+ 2 x ≤ 2 f(x)=4-x², 2<x<3 2x+b. 3 < x Find the value of a so that f(x) is continuous at 2. Find…

A: To find out the value of a as f(x) is continuous at 2.

Q: Evaluate the integral [x² In Select one: O -Inx-+C O O xả ln xdx nx - + C 9 None of them X 4 Inx-+C…

A: using integration by parts,

Q: Match the functions in Column A with their corresponding antiderivatives in Column B. Column A a.…

A: