61. det t sectdt d 62. du Jo Ix/dx 0 px [Hint: Use Definition 5.5.3(b).]

Q: List intervals on which the following function is INCREASING. Use INF for infinity, use no spaces,…

A: The given function,    fx=3x2-1

Q: Compute the area bounded by the curve x=y²-2y and the line x-y-4-0₁

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Q: Question 3 3x² + 5x + 2 Let f(x) 2x² + 71 4 This function has: 1) A y-intercept at the point 2)…

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Q: dx 1+tan x

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Q: Question 2 Consider the equation: 2²-11-12 A) First, use the "completing the square" process to…

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Q: NASA launches a rocket at t=0 seconds. Its height, in meters above sea-level, as a function of time…

A: Given; h(t)=-4.9t2+91t+164

Q: Question 7 Consider the Quadratic function f(x) = 9x² 4. Its vertex is ( Its largest z-intercept is…

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Q: Find the average rate of change of g(z) = 4x + 5 between the points (-4,-11) and (3,17)

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Q: Given : x³ sin(2x) dx = 277²-24 Find bif sb . 64 2π 3 5π 6 F|+ =|m 3 3π 4 sbst

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Q: Question 8 Let f(x) = (z - 6)² Find a domain on which f is one-to-one and non-decreasing. Find the…

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Q: Use the information given below to find sin (a-³). 12 tan a = with a in quadrant III I 5 3 cos B =…

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Q: Find the volume of the solid obtained by rotating about the y-axis the region bounded by y=2x^2-x^3…

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Q: Find a set of parametric equations of the line through the point (1,-2, 3) and perpendicular to the…

A: Concept: As we know that a equation of the line through the point (α,β,γ) and perpendicular to the…

Q: dx Arcsin (²) + c

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Q: Solve 4t² +8t+4= 0 by using the square root method. Hint: complete the square first! Enter each…

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Q: 1 sinx+cosx+1 -dx

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Q: dx 5. Evaluate the following tanº(x) cos4(x) tan'(x) [7tan²(x) +9] + C 36 tan(x) + =tan(x) + C…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: o evaluate (In x)² +3 dx,

A: answer is in next step  option C is correct

Q: Find T(t) and N(t) at the given point. x = T(0) N(0) = = = e cost, yet sint, z = e; t = 0

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Q: Using integration by parts, Then k is? (a) - 1.5136 ²x³ cos x³ cos(x²) dx = k - [*x sin(x²) dx 0…

A: Solve it

Q: If f cos42t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A, B, C and D are constants, ....…

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Q: Question 4 15x²x³43x - 19 The integral (x + 1)²(x² - 6x +13) Ax + B What is the value of ax²+bx+c²…

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Q: Using partial fraction in evaluating A 6-2x B 2x-6 © - ²7/ 1/1/2(2x + 1) = 7/7/2 Ⓒ - 1/2…

A: Solution of given question is written in below steps.

Q: Exatuate the integral QUS √3x xام واح

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Q: Find the limit. NOTE: Enter the answer using round brackets. t² +4 1 = lim t→+∞0 (?, ?) 4t² +5't

A: limt→∞t2+44t2+5, 1t

Q: what is the normal equation to the curve which is the circle with center at origin and and radius of…

A: Given circle , With center at origin (0,0) And a point on circle is (4,3)

Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 4 1 lim t+oo 5t² + 6'8t = (?, ?)

A: Solved below.

Q: (x + 2)(6x - 1) (6 - x)(4x + 2) Find the horizontal asymptote of f(x) = 4- y=

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Q: How long will it take for a $3000  investment to grow to $17,556 at an annual rate of 11% ,…

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Q: Using partial fraction in evaluating f(x) + What is f(x)? X x²+x+7* A 2x-6 7 ® 1/²(2x+1)= 1/²/2 B ©…

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Q: dx If S = is solved by trigonometric substitution, which of the following x² - 2x - 4 substitutions…

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Q: Use the formula k(t) k(t) = = ||r' (t) x r"(t)|| ||r' (t) ||³ = 10t. r(t) = e¹0ti + e-tj to find…

A: We have to find k(t)

Q: The IBP formula fudv=uv-fvdu Which of the following statements fits and satisfies the equations?…

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Q: [x-²sec (an ² (2) dx 7 2tan ²2 (²) - 7tan² ( 1 ) - ₁ X + C 77 11 2ten* (²) 2³(-).c 2tan X - + +C 11…

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Q: Calculate[ri(t) r₂(t)] and [r₁(t) × r2(t)] first by differentiating the product directly and then by…

A: This question can be solved using the concept of dot product and cross product of two vectors and…

Q: The IBP formula fudv-uv- - fvdu can also be written as fudv + ſ vdu = uv Which of the following…

A: Given that the four options  To find choose the correct option which is satisfi IBP formula

Q: 1. f (5x¹8x³ 2. f (4x + 2) de +6x² - 4x + 7) dx

A: Topic:- integration

Q: (A) = and B = . Find the vector projection of A D onto 2A - BO O O none of the above

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Q: Using trigonometric substitution to solve: sin 2x + C 8 cos x√3-cos²x sin 2x 4 cos x√4-sin²x secx 8…

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Q: y = 2 x + 2 -3+x

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Q: 19. TT/2 -π/2 sin 0 de 20. * sec² 0 de

A: 19 ∫-π/2π/2 sinθdθ [-cosθ ]-π/2π/2 0 - 0 =0 other way sin is odd function so also integration is = 0…

Q: Find sec 2x -dx. tan 2x cot82x (4sec 22x-1) (A) 12 1 1 I B 12 tan 2x 16 tan 82x Ⓒ -co1²2x-co1³21+ C…

A: Here is the solution

Q: Given: (1+2x) ex dx. Using integration by parts and letting u = -1-2x, dv = f(x)dx, then the value…

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Q: 60. (a) dx SI dt 1 + √t (b) de fint di dt

A: We can solve this as follows:

Q: 4. Evaluate the following sin(x)cos(2x)sin(3x) dx A. B. C. D. sin(3x) cos(3x) sin(2x) cos(2x)…

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Q: Use the formula k(t) k(t) = = ||r'(t) × r"(t)|| ||r' (t)||³ = 10t: r(t) = e¹⁰ti + e-tj to find k(t).

A: This question is related to vectors, we will solve it using given information.

Q: 1o. 1 |x-3|dx

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Q: Determine the number and type of solutions for the equation - 3x² + 14z 15 0 =

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