Find an equation for the tangent line to the curve parametrized by a = t¹ — 1 and y = t5 + t at the point t = -1.

Q: 11. Find two different antiderivatives of the function f(x) = 6x² +2ex. 1

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Q: Find the area of the shaded region. = √cos 20 9 cos X r

A: Area = integration of 1/2 (r2^2 - r1^2) d(theta)

Q: Let f(x) = x³ - 3x². Find the absolute minimum value of f(x) on the interval [1, 4].

A: The given function,  f(x)=x3-3x2 on the interval 1,4

Q: 2 Σ(-1)". n+1 n=1

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Q: d Calculate[r₁(t) · r₂(t)] and [r₁(t) × r₂(t)] first by differentiating dt dt the product directly…

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Q: "alse 1. The absolute extrema for a function f(x) will occur wherever f'(x) = 0 2. The rectangle…

A: Topic:- function

Q: The average cost function for the weekly manufacture of retro portable CD players is given by C(x)…

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Q: 7- Differentiate Y= f(g(x*)) h3(Vx)

A: Follow next step

Q: second derivative of y with respect to x from the parametric equations given 4) x=√1-t₁y = t³ - 3t…

A: We can find the required 2nd derivatives as below

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A: Given query is to find the velocity at indicated point.

Q: Evaluate the definite integral. NOTE: Enter the exact answer. 12 ti + t²idt = 0

A: To evaluate: ∫012t i+t2jdt

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

A: This is a problem related to vector calculus. Based on the general formula of green's theorem we…

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Q: 6) Given the function y = x³ - 3x. Find all the critical points, any local maximum or minimums, the…

A: 6)y=f(x)=x3-3xf'(x)=3x2-3f'(x)=0x2-1=0Critical points of f(x)     x=-1, x=1f'(x)=3(x2-1)f'(x)>0…

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

A: r1(t)=6t i+ 4t2 j+ 4t3 kdr1dt=6 i +8t j +12t2 kr2(t)=t4kdr2dt=4t3 k

Q: Two years ago, $5, 000.00 was placed into an investment in which the amount of money present, P,…

A: To find the amount of investment after 15 years from now.

Q: Suppose that z = x²y³, where both x and y are changing with time. At a certain instant when x = 2…

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Q: ∫(x2+5)2 dx Evaluate indefinite anti-differentiation

A: Let's find.

Q: dx x²+2x+5

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Q: Evaluate the line integral [39a²³yzds with respect to s along the 2 curve C: x = t, y t, y = t²,₁…

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Q: Suppose F(x, y) = -y sin(x)i + cos(x)j. (a) Find a vector parametric equation for the parabola y =…

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Q: lim (i-8j+² k) 4 lim (r 1-8j+² k) = 1+ 16

A: We have to find the limit

Q: Write √x+y²+2x-y=3 +y²+2x−y=3 as a polar equation r = f(0).

A: Write in Polar equation

Q: Find the absolute extrema of f on [-2, 3] if f(x) = x² - 6x - 1 O √5 O 2

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Q: Use Green's Theorem to evaluate F. dr, where F(x, y) = (y - cos y, x sin y) and C is the circle (x -…

A: Solved below.

Q: Consider the following. y = √x 4 X = 8 y = 2-x -6 -8 (a) Form the integral that represents the area…

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Q: Consider the function g defined as g(x) = { Evaluate the following limits. 1.) lim g(x) 3x+2 X-2…

A: limit of a function f(x) at a point x=a exists iff limx→a-f(x)=limx→a+f(x)

Q: 13 5 3 1 5 Let F= 1 7 -4 and G= -1 2 3 12 3 2 2 5 Find 5F- 4G. 5F - 4G = 00 C

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Q: 2. If the Profit function for producing x units is P(x) = 0.0035x³ + 120x, then the marginal profit…

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Q: Find T(t) and N(t) at the given point. r(t) = (t² − 3)i+tj; t=3 T(3): N(3) = =

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Q: (8x4 − 5x2 + 2)dx evaluate indefinite anti-differentiation

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Q: Calculate the perimeter of each of the following [4] a) a parallelogram quit piece with sides 6%…

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Q: Consider a triangle ABC like the one below. Suppose that A = 65°, B=55°, and c=40. (The figure is…

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Q: The weekly sales of Honolulu Red Oranges is given by q = 980-10p. Calculate the price elasticity of…

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Q: Consider the following. (1, 1) 2 6 10 X 4 X=8 -4 y = 2-x -6 -8F (a) Form the integral that…

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Q: Find dy/dt using the given values. dy dt y = x² - 6x for x = 1, dx/dt = 3.

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Q: Question 9 In MN = In M + ln N Maybe False True None of these

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Q: 4. Evaluate lim (cos x)¹/x². x-0

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Q: answer

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Q: D(x) = 62-0.1x

A: answer is in next step

Q: 10 cm K L h cm 6 cm LL 11 cm Part 1: Part 2: Part 3: Part 4: Let ʼn be the height of AJKL. Find the…

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Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

A: Given that the daily profit (in dollars) from the production and sales of x units of a product is…

Q: T: P2 P₂ defined by T(a + bx + cx2) = a + b(x + 8) + b(x + 8)² Find the following images of the…

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Q: cos( sin 8x 8 Also, u = x. Therefore, the differential is du = dx dr Step 2 To find the integral J x…

A: A detailed solution is given below.

Q: Let f(x) = 3x5 - 5x³.

A: As per our guideline we are supposed to be answer only first three subpart of the question you can…

Q: Section 6.2 Volumes 1)(6pts) Find the volume of the solid obtained by rotating the region bounded by…

A: Given y=2-x^2, y=1 ; about the line y=1

Q: A) ( This problem consists of two parts. Evaluate the following indefinite integral 5 TVER _ln(x+1)…

A: To evaluate: ∫51-x2+x21+x3+lnx+1x+1dx Let I = ∫51-x2+x21+x3+lnx+1x+1dx I =…

Q: Consider the system of equations x₁ − 2x₂ + 3x₂ = 1 - 2x₁ - 3x₂ - 2x₂ = 3 x₁ - x₂ = 5x₂ = 2 a.…

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Q: d. Sketch the piecewise function x²2x-5 -4 ≤ x < 7 F(x) = 30 - 7 ≤ x ≤ 12 -x + 72 5 e. Describe the…

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Q: 1. Find the area of the region enclosed by the given curves. a) y - x² = 2x and x + 4 = y b) x = y¹,…

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