15x²x³43x - 19 can be rewritten as (x + 1)²(x² - 6x +13) Ax + B C D Slax ² + + lax² + bx+c (mx + n)t rx + s Ax + B S ? ax² + bx+c + In|x² - 6x + 13| (b) Arctan (³) - In|x² - 6x + 13| (d) Inx² - 6x + 13| The integral What is the value of (x-3 (a) Arctan (c) Arctan (³)

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A: Use root test to check the convergence of series.

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A:

Q: lim (2x²+x-1) 2-0 LIMIT VALUE: 2²-4 lim 2-0 2+8 LIMIT VALUE: LIMIT VALUE: 9-z lim 2-9 3-√√2

A:

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A: Use Lagrange theorem

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A: Given Admission to baseball game is $2.5 for general admission and $4.5 for reserved seatsThe…

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A:

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A: Given,  f(x)=4x2+5x

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A:

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A: Solution is here

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A:

Q: What can you say about the series Σan in each of the following cases using the Ratio Test? Answer…

A:

Q: 3 Find f such that f'(x) = - √x f(x) = f(1) = 12.

A: Solve for the f(x)

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A: topic - limits a3+b3=(a+b)(a2+b2-ab)

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A: Given is the application based question of integration.

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A:

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A: We can find the exact answer as below

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A: To use integration by parts for ∫x sec-1(x) dx

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A:

Q: a) √ (³x²-²) dx S (3x2

A: In this question we have to find integration and after that We have to verify.

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A: limx→∞ex21-x3Apply L-Hospital rulelimx→∞2xex2-3x2limx→∞2ex2-3x

Q: || ti + t²j||dt|

A: Explanation of the answer is as follows

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A:

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A: Solving

Q: Q3: Find gradient of the following function at given point 1) f(x,y)=y-x, (2.1) 2) g(x,y)=y-x²,…

A: As per as our guidelines i am supposed to answer only three part of this question.

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A:

Q: 2. Find a power series solution of the differential equation y' = 4y

A: To find a power series solution of the following differential equation.y'=4y

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A: This question can be solved using the concept of differentiation and limits.

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A:

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A:

Q: If t is in years, and t = 0 is January 1, 2005, worldwide energy consumption, r, in quadrillion…

A: We need to solve integral porblem.

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A: To find the value of y' at (3,-3).

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

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A: Given query is to find the graph of the function.

Q: Use the properties of natural logarithms to simplify the expression. In(e) П

A:

Q: Calculate the derivative. f(x) = 6-9x1/3 +9e* (Use symbolic notation and fractions where needed.) d…

A: A detailed solution is given below

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A:

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A: We have to estimate the error in computing the length of the hypotenuse.

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A:

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Q: f(x) = t^2(t - 7)^1/3.   Find all critiacal points and all relative maxima

A: Solution is given below:

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A: topic - functions and derivatives

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A: Answer is in step 2.

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A: Solving the problem by finding the value of compound interest.

Q: (a) f(x) = 2x³ + 3x² - 12

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question..…

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A: Given query is to find the derivative and the tangent equation.

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A: Given ,  A cat darts around a room chasing a ball. the cat first travels along the vector < -1, 2…

Q: 1) x² + y² + ² = 3, P. (1,1,1) 2) 2=-x²=0, P. (2,0,2) XZ 3) cos(x)=x²y + e + yz = 4, P. (0,1,2)

A:

Q: 16. What is the derivative of the function: * y = sin(6x² - 1) y = 12x cos(6x² - 1) y' = x cos(6x² -…

A: Solving the problem by finding the value of the derivative.

Q: The series ∞ (-10) k k! k=1 is an alternating series but we can apply the ratio test to ∞ (-10) k k!…

A: We have to check convergence of series with the help of ratio test.