Let fa)=S(-5-x2 + 23x +19 f Xチー6 if X= -6 calculate the following limits. ENter DNE if the liniit does notexist lim こ X>-6 f(-6)=

Q: y8. |cosx-sinx|dx 16. J-

A: To integrate.

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A: To determine whether the given series is convergent or divergent.

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A: arc length

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A: f'(t) &gt; 0 imply function increase with time.  f"(t)&lt; 0 imply function is concave downward

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Q: Find the arc length L of the graph of r(t). r(1) = t³ i+ t j+V6r? k, 2 <t< 5 k, 2 <t < 5 L = i

A: Given : r(t) = t3 i + t j + √6 t2/2 k 2 ≤ t ≤ 5 Now, r'(t) = 3t2 i + j + √6 t k Arc Length :

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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: Suppose that a, b, and c are unknown constants such that f(x) = x² + ax + b and g(x) = e(3z–3) %3D…

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Q: if x 2 a) Evaluate each of the following, if it exists. (If an answer does not exist, enter DNE.)…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 8 cos(t)i +3 sin(t)j +…

A: Solution is given below:

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Q: (3x-2)cx In the integration --17 what integration method is appropriate? a. Integration by Power…

A: Use integral methods

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Q: Evaluate (2x – y) dx + (x + 9y) dy. C: x-axis from (o, 0) to (0, -9) and (0, -9) to (9, -9)

A: We will evaluate the given integral as shown below

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A: To find the equation of family of curves whose slope is given .

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A: We need to find cartesian coordinates.

Q: 1. Find the solution to the system 4x - Зу +3z %3D 0 2х — Зу + 2z%3 0 бх — 12у + 7z 3D0.

A: “Since you have asked multiple Questions, we will solve the first question for you. If you want any…

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A: We can evaluate the given integral by using the substitution u = x⅙  and the following formulas.

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Q: Ex: Show that if v, u, w are any vectors, then (H.W.) ux (v x w) + v x (w x u) +w x (u x v) = 0.

A: Dot Product Property :- a.b = b.a = a*b*cosθ

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A: here is the solution:

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Q: Question 2 A balloon is rising vertically over a point A on the ground at the rate of 15 feet per…

A: Using differentiation

Q: Q9. Which of these is not the derivative of the function, y = x": A. -½x1½ В. — 0.5х-1Vx-1 С. -0.5 1…

A: This is a problem related to differentiation of the function. Based on the general formula and…

Q: 1. For which function below does lim f(x) = -∞? X-2+ 1 f(x) = - x-2 1 f(x) = - (2 – x) x² - 4 a. с.…

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

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Q: Evaluate F. dr. F(x, y) = 7xi + 4yj C: r(t) = ti + V4 - tj, -1 sts

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Q: H.W: which series converge and which diverge: 1. E 1 1 2. n=1 n=1

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Q: 10. Consider the system of equations X, - 2x, + 3x, = 1 2х, — Зх, — 2х, 3 3 X, - x, - 5x, = 2 a.…

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Q: Use Green's Theorem to evaluate the line integral. Iy? dx + xy C: boundary of the region lying…

A: A detailed solution is given below

Q: 3x+2 dy for y = In, dx 2. Find Fully simplify your answer 3x-2

A: Solving the problem by finding the derivative.

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

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A: We have to solve above question

Q: Find the area of tge region bounded by the loop of y^2 = x(5-x)^2 -about plane area, complete…

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