Write the partial fraction decomposition of the given rational expression. (x- 3) (x + 5) What is the partial fraction decomposition? (x – 3) (x + 5)

Q: Find the Taylor series generated by f at x = a. f(x) = e*, a = 10 i e10 (x - 10)n+1 n! n=0 e10 (x -…

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Q: Find the solution of the following Differential Equations 11) y"-4y'+4y= 0, y(0) = 2.1, y'(0) = 3.9

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A: This question is based on exponential Function.

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A: It is given that, a rectangular garden is fenced on three sides, and the house forms the fourth…

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A: The given series,       ∑k=1∞(-1)k+1k+6 5k

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A: Take a partial fraction

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A: first we will take x common from numerator and denominator, then take limit.

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Q: 6 Evaluate the limits lim: X+ co X 6.

A: Topic:-   limits and continuity

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Q: What is the square root of -5?

A: Here we have to find the -5

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A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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A: To show that the function f defined by fx, y=1, x, y=1, -1x2+yx+y, x, y≠1, -1is not continuous at 1,…

Q: Evaluate the difference quotient fla + h) – fla) for the function f(x) = 2x²- 3. 4а + 2h 4а + 2h - 6…

A: Given: f(x)=2x2-3

Q: S L-1 s2-4s+13)

A: Rewrite

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Q: the function below f(x, y) = 2x² – 3y – 4

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Q: Evaluate the difference quotient fla+k) - fla) for the function fx) = 5x. %3D 1 5h

A: We can find the difference quotient

Q: 2. S

A: Given :∫xdxx2-4x-7

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A: Here we have to use the Runge-Kutta 4th order method

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A: Explanation of the answer is as follows

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Q: 5TT 2. Cos 6. 2п Cos 3 + sin sin 6 - - - 3 一。

A:

Q: a) Determine whether the series 11n? + 8n + 32 is n³ + 3n² – 7n+ 1 n=1 convergent or divergent. b)…

A: !) The given series is: ∑n=1∞11n2+8n+32n3+3n2-7n+1 Let, an=11n2+8n+32n3+3n2-7n+1; n≥1&amp; bn=1n;…

Q: If D is the triangle with vertices (0,0), (55,0), (55,49), then dA=

A: double integration

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A: I have appended the formula used in the solution part.

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Q: so Je cos T0 d0

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Q: (3) Is f(x) = 2x a solution to the differential equation f(x)–xf'(x) = 0? Explain briefly. %3D

A: The differential equation is f(x)-x·f'(x)=0

Q: 4. Find the derivatives of the following functions. Do not simplify your answer! d (a) dx V +1 sec x…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: If 2(-1)" a, is absolutely convergente the n=0 na, is divergente. Select one: O True O False

A: Topic:- sequence and series

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Q: Vx2 – 2x – 3x 4. lim 4х + 5 I -00

A: Answer Number (4):  To evaluate the given limit without using L'Hospital's rule.limx→-∞x2-2x-3x4x+5

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A: X coordinate

Q: Use the Alternating Series Test to determine whether the alte S(-1)k+1_ k 7k + 8 00 k k = 1 Identify…

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Q: Consider the curve C of equation (x² - y + y?)2 = x² + y? . Among the indicated options, select the…

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Q: a) Determine whether the series Σ is convergent or Vn3 + 4n + 5 n=1 divergent. b) Determine whether…

A: We have to find if the given series is convergent or divergent.