(ii) Find all values of k for which the integral fo (+)da converges and evaluate the integral at those values of k.

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Q: 10. Find a Maclaurin series which represents cos(x) for every real number around the point a = 0.

A: As we know the Maclaurin series;  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+fiva4!x-a4..... Where…

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Q: Evaluate the integral and check your answer by differentiating. NOTE: Enter the exact answer. 1…

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Q: 2) A) (::.. y" + 9y = 0 B) i y" + 9y = 0, y(0) = 0, or else show that it has no solution ... )…

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Q: Given the following graph of f(x), state --6-5-4-3-2-1 3- 2+ 3 4 a) the domain b) the range

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Q: The series verges Justification: (converges, diverges) by applying the test.

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Q: 2. Let f(x) = nx² - 2x + 5 and g(x) = 6x² - 5x + m. The functions are combined to form the new…

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A: The given curve and the point is x=sin(t), y=cos2(t) ; 32,14

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Q: 3. y" +4y'+4y=0 __(Use reduction of order method)

A: the auxiliary equation is  m2+4m+4=0(m+2)2=0 m+2=0m=-2

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A: We will calculate the domain and range.

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Q: Use the graph to determine the limit. (If an answer does not exist, enter DNE.) -8 (a) lim f(x) =…

A: To find out the limits.

Q: Find the limit (If It exists). (If an answer does not exist, enter DNE.) (x² - 4x +18, -x² + 4x -…

A: Put the condition for existence of a limit and cross check.

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A: See this solution in below

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Q: The function f(x, y) = -2x² + 4y? - 11 has a local minimum at the point (0, 0). Select one: O True O…

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Q: Find the limit. lim (3x-4)

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Q: Give an example of a function f (x) that has one  positive derivatives on the range (−1, 0) and a…

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Q: ;) Choose/box the correct statement. To evaluate x³ 3x² +1 dx x²-1 we begin the calculation by A.…

A: This question can be solved using the concept of decomposition of improper rational function.

Q: Use the given graph of f(x) to find the intervals on which f'(x) > 0. Q Ay 25- 20- 15- 10- 5A…

A: given,

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A: We have to find parametric equation.

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Q: A) (:: :) Verify that y = c₁cos(3x) + c₂sin(3x) is a solution of y' +9y = 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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Q: Use an iterated integral to find the area of the region bounded by 2x - 5y = 0, x+y=6, y = 0.

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Q: Evaluate the integral with the aid of an appropriate u-substitution. Simplify the answer, if…

A: In this question we have to solve the Integral.

Q: 8. Eliminate the parameter to find a Cartesian equation of the curve: x(t) = t, and y(t) = 3t+4, t≥…

A: To eliminate the pararmeter to find a Cartesian equation of the curve: xt=t, and yt=3t+4, t≥0.To…

Q: Find the derivative. 2 f(x) = 4√√8x² +9 f'(x) =

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Q: F(x, y, z) = yzi + xzj + xyk (a) C₁: r₁(t) = ti + 3j+ tk, 0≤ t ≤9 (b) C₂: r₂(t) = t²i + tj + t²k, 0≤…

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Q: Evaluate the line integral along the given path. S ² + y² + 2²) ds C: r(t) = sin(t)i + cos(t)j + 7k…

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Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of t…

A: Please see the below picture for detailed solution.