Step 1 To find the definite Integral 9 dx by the limit definition, divide the Interval [2, 7] Into n sublntervals. Then the width of each Interval Is b- a 7 2 Ax = %3D Note that A- as n- o.

Q: F(x) = dt Step 1 Rewrite the glven functlon F(x) D, -2 dt as F(x) =D -2t dt.

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Q: 3. Find the binomial series for (1+x)3 4. Use the result in problem 3 to give a power series…

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Q: Setup the iterated integral using the order dydx and dxdy. Sketch R. // (Va+ e") dA where R= {(x, y)…

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Q: 3. For curve y ==x +4x2 - 12x , locate the possible maximum and minimum %3D points.

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Q: dy 15. Vx eu+ Vx, dx x > 0

A: We have to solve the difference equations

Q: Determine the signs (positive, negative, or zero) of y = f(x) (shown in the graph) and f'æ) and…

A: Consider the graph

Q: 2. Write the given (total) area as an integral. a. The area above the x – axis and below y = 4 – x2…

A: Let's find.

Q: Use series to evaluate the limit. 4 3 sin(2x) – 2x + lim 4/3

A: Given problem:-

Q: A mass attached to a vertical spring has position function given by 8(t) = 4 sin(4t) where t is…

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Q: Determine convergence or divergence of the alternating series. 24) E (-1)n 6n5 + 5 n = 1

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Q: 8. A 25-ft ladder is placed against a building resting on a banana peel. The base of the ladder is…

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Q: Determine the intervals on which the given function is concave up or concave down and find the…

A: Solve the following

Q: Evaluate the limit 5+ 9x lim 1+00 3 – 4x

A: Given problem:-

Q: Problem 3. at a speed of 60 cm/s. Suppose the function g models the radius as a function of time t…

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Q: 24) Identifa tue internel of convergen ce of a power ser's Ž (3)" n-1 (-3)", n=) a ) b) c) d) 3 2x23…

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Q: dx 9- x 15.

A: Topic = Integration As per guidelines , At  a time only one question can be answered out of…

Q: (А) True B) False

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Q: Give inequalities for r and 0 which describe the region below in polar coordinates. (Click on the…

A: Angle is given by arctan(y/x)

Q: (a) Find the value of P(?, 4) and P(?, 6) using permutation formula, where ? is the last two digits…

A: Permutation: Permutation:  The permutation is a method of arranging objects in a specific order.…

Q: Find the derivative of: 3 sin (– 3x). Hint: sin (x) = [sin(x)]"...so use the chain rule (twice!).

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Q: d) Use the right endpoint rule to approximate the area under the curve of f(x) = 4- x2 on [1,2]…

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Q: alyze and sketch a graph of the function. Find any intercepts, relative extrema, and points of…

A: We are allow to solve one question and 3 subpart only at a time. If you want rest of solution please…

Q: Find f'(2).

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Q: help

A: We will solve the Differential equation.

Q: Let F(x) = f(x*) and G(x) = (f(x)). You also know that a' = 5, f(@) = 3, f'(a) = 13, f () = 1 Then…

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Q: 2 | (ax³+ = 2b - bx²+cx) dx x?dx . -2 (A) True B False

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Q: 5. Consider the region R in the plane enclosed by x-0, y=1 and y = x a. Draw the region b. Use…

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Q: 2 2 2 2 4' 16' 64' 256' 1024

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Q: Graph the problem and solve using vertical or horizontal rectangle. Show your solution. 1. Find the…

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Q: 16. Given: [ S(x)dx=10; s(=)d& x = ? (x)dx= 3;

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Q: y = xx, x 4, and y = 0 Revolve the area of the shaded region about the line x = 4. Using circula…

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Q: Fit a second degree parabola y = ax² + bx + c to the following data %3D 3. y 1.8 1.3 2.5 6.3

A: Normal equations associated with y=ax2+bx+c are: ∑y = a∑x2+b∑x+nc ∑xy=a∑x3+b∑x2+c∑x…

Q: Verify that the conclusion of Clairaut's theorem holds, that is, u, Uxy = "yx' u = x'y8 – y? With u…

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Q: A ball is thrown into the air and its position is given by h(t) = - 4.3t2 + 41t + 15 where h is the…

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Q: Find an explicit formula for an. 1 1 4'9' 1 1 14) 1, 16' 25

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Q: Evaluate the defınite integral. e? i +ej+t k)dt e? i + (e- - 1) j+1 k 7 e? - 1 i - (e- - 1) j+ 1 k 7…

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Q: A. (, 글) %3 ( B. (- , -) =(

A: We will find the coordinates in polar form.

Q: A job applicant estimates that his chance of passing a qualifying examination is , and his chance of…

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Q: Determina the vector field of F. F(1, y) = yi -j

A: Please see the below picture for solution.

Q: e equation (2 cose – 1)(3 + tane) = 0 over the interval [0, 27]. solving for trig functions,…

A: We will solve the equation.

Q: If f is just that = e*[- sin(x + y) + cos(x +y)] and -e sin(x+y) which if the %3D ay following is…

A: On solving this we will get:- Option (A) is correct.

Q: The area bounded by y =3Vx and 2y =3x is revolved about the x-axis. Using cylindrical shell method,…

A: Solve the following

Q: 4- to --6 -5 -4 -3 -2 -1 5- ver which interval of z values is f'> 0? о (2, о) O 12, 0) 0(- 00, 2)…

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Q: 3873727x3737

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Q: 1. Find the area of the region bounded by the given curves. Show the computed areas of sections…

A: Let's find.

Q: Let f(x) = Vx? + 9. Then f'(x) is f'(1) is f"(x) is and f'"(1) is

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Q: 16 Indicate the general rule for the arithmetic sequence with a3 = 8 and a8 = 33. a n = 2 + (n -…

A: The nth term of an arithmetic sequence is an = a + (n - 1)d  a is the first term. d is the common…

Q: Determine the vector field of F. F(x, y) = yi – xj

A: Given:     F(x,y) = yi - xj.          ---------(i) We have to determine the vector field of equation…

Q: show

A: As per the guidelines we can solve 3 parts only.

Q: Determine whether the sequence converges or diverges, and, if it converges, find lim an: n-00 3 - 1n…

A: We have to find the limit