Evaluate the definite integral. NOTE: Enter the exact answer. •3 ti + ti dt

Q: 10. At what point on the parabola y = 3 x 2 + 2xisthetangentlineparallel totheline y = 10x -2? Use…

A: Given query is to find the point where tangent line to the parabola is parallel to the given line.

Q: Find an equation for the tangent line to the curve parametrized by x = 4t y = est at the point t =…

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Q: Determine a, and as for each arithmetic sequence. See Examples 3 and 4. 29,. 24. -3, -7, -11,... 25.…

A: Since, the student has mentioned to solve only question number 24, so we are solving accordingly…

Q: Find all rational zeros of the polynomial, and then find the irrational zeros, if any. Whenever…

A: Solution:

Q: Evaluate the function at the indicated value of x. Round your result to three decimal places.…

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Q: Find the derivative of g(x) = fecost dt.

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Q: Is there a number a such that the following limit exists? (If an answer does not exist, enter DNE.)…

A: Given;  limx--2 (4x2+ax+a+12)/(x2+x-2).

Q: c. The area between y sin x and the x – axis for 0 < x< a

A: Area between the y=sinx and x axis from x=0 to x=π

Q: Find the derivative of the function. f(x) = (5x + 7)³ (06² +00) ² f1(x)

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Q: 1. Graph the system of inequalities 2х + у S 50 4х + 5y < 160 x 2 0, y 2 0

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Q: Find an equation for the tangent line to the curve parametrized by a = t¹ — 1 and y = t5 + t at the…

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Q: 17. r=3sin 40

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Q: Vertical and Horizontal area of the plane region y=2x^2+1 and y=x^2+5

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Q: Evaluate the definite integral. Si f (x) dæ, f (x) =4"-(7a+ 13)/a?

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Q: Use Descartes' Rule of Signs to determine how many positive and how many negative real zeros the…

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Q: The displacement (in meters) of a particle moving in a straight line is given by s = 2t3 where t is…

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Q: 3. [_x dx √2 +*

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Q: In Exercises 33-42, determine if the given vector field has a potential. If so, find one. 34.…

A: Solved below

Q: Solve the inequality R(x) <0, where x-3 R(x) = x(x-4)' function. 4- 2- , by using the graph of the 6…

A: Here we have to find the inequality by using the graph.

Q: a. Find the slant asymptote of the graph of the rational function. b. Follow the seven-step strategy…

A: We need to find slant asymptote.

Q: Suppose that f(x) = -9x/6. Evaluate each of the following: f'(2) = f'(5) =

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Q: Verify Green's Theorem by evaluating both integrals y² dx + x² dy = / dA дх ду for the given path.…

A: Here we have to verify the Green's theorem.

Q: Suppose that f(x, y) is differentiable at the point (3, 1) with f(3, 1) = 4, fx (3, 1) = 2, and fy…

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Q: csc z) Evaluate: lim (x² + e¬®)@¯

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Q: Graph the function using translations. f(x) = 3x+1

A: We will find the suitable graph.

Q: Find the length of the curve parameterized by x = 2 + 3t² and y = 3 + 2t³ from t = 0 to t = 3.

A: To find the length of the curve parameterized by x=2+3t2 and y=3+2t3 from t=0 to t=3.

Q: A theatre has a seating capacity of 250. The ticket prices for children and adults are $8.00 and…

A: Let 'x' be the number of  children's and 'y' be the number of adults. Now x≥0 and y≥0 since the…

Q: Consider the curve parameterized by x = 2t³ - 33t² + 180t and y = 2t³ + 33t² + 180t. At what points…

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Q: The volume of a right circular cone of radius a and height y is given by V = dy volume of the cone…

A: Explained below

Q: 7. Find the slope of the tangent line at point (-2,2) on the curve f(x) = 2x² + 3x using First…

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Q: The equation of motion of a particle is s = t4 - 3t3 + t2 – t, where s is in meters and t is in…

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Q: 8. Find the derivative of the function f(x) = x ² - 10x + 3 using First Principles.

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Q: lim (- 3" n→+00

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Q: The car you are interested in has 16 color options, 3 engine choices, and 6 entertainment system…

A: Given ,  The car you are interested in has 16 color options , 3 engine choices , and 6 entertainment…

Q: 3 Dax has a banner that is 7 feet long and 5 feet wide. He wants to make a new banner that has the…

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: 7. Find the partial fraction decompositions of the following rational expressions. a) b) (x²+11x) dx…

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Q: MP USING TOOLS Use a fraction or a mixed number to represent the tiT on a number line. Let 0…

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Q: Integrating factr: (y -x + xy cotx)dx + xdy= 0(*). Determination of integrating factor for egn of…

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Q: 5. a. Evaluate lim(3x³ +7x−16). b. What is the meaning of this value?

A: Given;  limx-2(3x3+7x-16).

Q: Find the k component of (curl F) for the following vector field on the plane F=(xe^2y)i + (8ye^x)j

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Q: 1.) lim 5-x 2.) lim 5-x 3.) lim 5-x

A: Given query is to find indicated limit.

Q: Verify Green's Theorem by evaluating both integrals aN v? dx + x² dy | dA ду ax for the given path.…

A: Given problem:-

Q: 2. Use local linear approximation to estimate (31.62). Th

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Q: Find g'(3) given that f(3) = -2, f'(3) = 4 , and g(x) = . 2x+1_ f(x) * Answer:

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

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Q: √x²√9 - x² dx

A: We will solve the integration,

Q: ||r'(t) × x r" (t)|| Use the formula k(t) to find k(t). r(t) = t’i + tl5j %3D K(t) :

A: The given formula is; κt=r't×r''tr't3 And rt=t2i+t15j   As we know that; The Power law; ddxxn=nxn-1

Q: Use the indicated method to approximate the area under the curve f(x) = x³ + 28 on the interval [-3,…

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Q: What is the summation from n = 1 to infinity, of  (3^(n+1)) / 5^n + 1 ?

A: Given that,       ∑n=1∞3n+15n+1

Q: 4x - 82 6х — 10

A: