Evaluate the following a) lim t-16

Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and f'(0) = 8,…

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Q: Find the nth Taylor polynomial for the function, centered at c. 1 f(x) n = 4, c = 2 +2² P4(x) = = =

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Q: Which of the following statements is CORRECT? x³ + x 1 = 0 has no solution in [0, 2] Ox³ + x-1=0 has…

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Q: Find the arclength of r(t)= on the interval from t equals zero tot equals 2 times pi.

A: Given:  r(t)=<5cot(t), 3 sin(t), 4 sin(t)>To find:  Arc length form t=0 to t=2π

Q: Find a tight upper bound for the approximation to * cos(z) cos(x) Note that the second derivative of…

A: Concept: Midpoint rule: Assume f(x) is a continuous function on [a,b]. Let n be a positive integer…

Q: For each of the questions below, indicate if the statement is true (T) or false (F). (a) Any…

A: Note:- according to the company policy we can do only 3 subparts of a question so please upload the…

Q: a. Determine the Cartesian equation of the plane that has x-, y-, and z-intercepts at 2, -4, and 3…

A: Here we will find all equations,

Q: (3x²-3x-4) 2x²-3

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Q: Given that f(-10) = -0.1 and f(-9.6) = 1.8, approximate f'(-10). f'(-10)

A: We know, f'(x)=f(x+∆x)-f(∆x)∆x Let, x=-10 and ∆x=0.4

Q: 4. · [ (8x − 3) (4x² – 3x) ³ da x J dx - 4x² x S dx 3 - 5x² 5. 6.

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Q: ds a) If distance s = e-2t sin(3t) m find velocity v = when t = 0.2 s dt b) If current is given by i…

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Q: 370 0 3sin²2x dx

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Q: 5. r(x, y) = ln (x + y)

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Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

A: Solution

Q: items 12-15, consider the region bounded by the curve y = cosx and the x-axis, where 0 ≤ x ≤ What is…

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Q: y = cos((pix)8)

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Q: S x² √x²+4 dx

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Q: Question 1. (5 marks) Find the distance between the point A = (2,2,3) and the line L : x = -1-4t, y…

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Q: (a) Use the Maclaurin series, In(1 + x) = x -+-+ = E=1(−1)n+12², 2 X to derive the series expansion…

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Q: 1. 2y"" Hardcore 0 7y"+12y + 8y

A: To solve the given differential equation.2y'''-7y''+12y'+8y=0

Q: (B) Use Tabular integration to evaluate the following: - f(t³ - 4t² + 5t + 32)sin(t)dt

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Q: Show that the points form the vertices of the polygon. isosceles triangle:     (4, −4), (5, 2),…

A: Solve the following

Q: Given the graph of the function f(x), answer the following question. B C F D -20 -10 A E -10 Of the…

A: Solution is here

Q: (b) Find the area under the curve defined parametrically as x=t²-1 and y=t³-t for 0≤t≤1

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Q: 7. y - 5y + 7y" - 5y' + 6y = x² + 3x - 5 Ans: y = C₁e³x + C₂e²x + C3 cos x + C₁ sin x + x² + ²x -…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Figure out the generated volume of rotation the region surrounded by = 4x² and y=4x about X-axis.

A: find intersection point

Q: Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures…

A: Let's solve.

Q: (y¹x=i+ I 7² +11 -)dx + N(x,y)dy = 0

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Q: Q1: If the function f(x) define as f: R →R such that f(x)= (x+1, x>2 x²-1, x≤2 Show that the…

A: Solution is given below:

Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and ƒ'(0) = 8,…

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Q: •S√6 3. 2 √6-x² dx

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Q: Find the distance between the points. (Round your answer to two decimal places.) (9.1, −2.6),…

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Q: The yearly demand function for Penn State Bakery cookie trays is given by x² + 5p2 + 7x + 10p = 290…

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Q: 4 fsin 2xcos²2xdx

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Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t + 32) sin(t)dt

A: We can evaluate the given integral by using the tabular integration.

Q: Find a formula for the quadratic function whose graph is shown. y X 15 f(x) = -5 30 20 10 f 5 (5,2)…

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Q: f" (1) =

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Q: Differentiate r(t)=

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Q: Find the tangent line approximation for √1 + x near x = 5. y = |

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Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

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Q: 3 4 3η ΣΣ (+1) j=1 k=0

A: A detailed solution is given below.

Q: 1. S √x dx VX +1

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Q: (-1)n+1 Given that ³²= 24 x²n. Obtain the power series representation of each of the following 9+x²…

A: Given: Now,           -39+x2' =-319+x2' =-39+x2-1' =-19+x229+x2' =-3-19+x22· 2x=6x9+x22

Q: Q 19 If a fault cuts three sides of a quadrilateral, then: Red with one of the vertices 2- Cut the…

A: Given question:- 19) if a fault cuts three sides of a quadrilateral then,

Q: C. Find the volume of the solid generated by revolving the area bounded by the given curves about…

A: Let's find volume of solid.

Q: 3. Emily is making a closed rectangular box with a square base from two different woods. The wood…

A: Use minimizing concept

Q: Find the radius of convergence of the power series. (If you need to use oo or -00, enter INFINITY or…

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Q: 2. A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F.…

A: It is required to find the initial temperature of the inside room using the given conditions…

Q: PART I. Calculating First Order Partial Derivatives 1. f(x, y) = 2x² - 3y - 4 3. f(x, y) = (x² -…

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Q: Differentiate the following function. f(x) = -3e-3x d -(-3e-³x) = dx

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