Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) I =

Q: Evaluate the indefinite integral. 8 + x*dx + C

A: topic- indefinite integral

Q: Consider the limits. lim f(x) = 5 x→7 lim g(x) = -12 x→7 Evaluate the limit using the limit law for…

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Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x 450. c and y = c – x² is…

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Q: Evaluate the limit. 12 lim x-5 x2 + 2x – 35 5 Give your answer in exact form. If the limit does not…

A: topic - limits

Q: Solve y" +3y'+2y =

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Q: 2. Write the Riemann sum to find the area under the graph of the function f(x) = x* from x = 5 tox =…

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Q: The current population of a small town is 2376 people. It is believed that town's population is…

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Q: Find the slope of the tangent line to the curve y = (1+ 4x)7 at the point x = 2. %3D

A: Slope of the tangent line is obtained by just derivative of the function  wrt the independent…

Q: Solve the given initial-value problem y' + (tanx)y = cos?x, y(0) = -1

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Q: ローペープ 8-x²-y z?dzdxdy. Use cylindrical or spherical coordinates to evaluate the integral.

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. da dz dy = y -54 J-36 %3D

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Q: pproximate using differentation:  e0.99 Please show step by step solution.

A: This question can be solved using the concept of approximation using derivatives.

Q: Find the solution of the following linear ODE given that y(5)=3 dy Зу = (x – 4)² х—4 dx

A: Use integrating factor for the differential equation.

Q: Compute the derivative of the function y = 6 cos- (4x) at the point x = (Use symbolic notation and…

A: Solution ) y = 6 cos-14x Differentiate with respect to x  y' = 6 d/dx (cos-14x) [ we know that  d/dx…

Q: 125 and y = 10. y? y = x, x =

A: answer is in next step

Q: Find the solution of the following BVP given that y(0)=2 and y(1)=0. d’y_12dy. dx +36y = 0 dx

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Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A: To find maxima/minima of the function: f(x,y)=x2+2y2-3xy with constraint g(x,y)=x+y-24=0

Q: Problem 5 Find the Maclaurin series for f(x) and its associated radius of convergence. (a) f(x) =…

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Q: Consider the equation ay" + 4y' + cy = 0 the constants a,c,m are real and different from zero, the…

A: Solve the differential equation

Q: Use Green Theorem to Evaluate |y x²dx – x²dy where C is left half of x² + y² = 25

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Q: V4-x? 3-x2-y² Evaluate the iterated integral. x dz dy dx -5+x2+y? A 128/15 16/89 23/6

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Q: d Calculate ri(t) · r2(t)] and r1(t) × r2(t)] first by differentiating d dt dt the product directly…

A: r1(t)=cost i+sint j +3t kdr1dt=-sint i+ cost j+3 kr2(t)=2i +t kdr2dt=k

Q: Evaluate the double integral over the rectangular region R. / 8xy°dA; R = {(x, y): – 1 < x < 1, – 7…

A: Given:       ∬R8xy6dA   R=x,y: -1≤x≤1 , -7≤y≤7        ∬Rfx,ydA=∫ab∫cdfx,ydydx…

Q: Find the limit. lim (t i - 8 j+ 1? k) k lim (t i-8 j+t k) = j+ i i+ i 1-2

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Q: If g(x) J.J S. 1 -dt , find g'(2).

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Q: ||r'(t) × r"(t)|| ||r(t)||° Use the formula k(t) to find k(t). 3 r(t) = t'i + tºj %3| K(t) =

A: Use the given formula and find the required expression.

Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: Find the volume V of the described solid S. A right circular cone with height 3h and base radius 4r…

A: Solving the problem by finding the volume of the cone.

Q: The integral TT tan x sec?x dx O none of them is an impróper integral of type I that diverges is an…

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Q: Find the centroid of the region R bounded by the graphs of y = x² and y = 1.

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Q: Find T(t) and N(t) at the given point. = e' cos t, y = e' sin t, z = e'; t= 0

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Q: Find the arc length of the parametric curve. x = e', y = et, z = V2t; 0<t< 4 L = 54.6

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Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

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Q: x2 - 16 dx

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Q: Sketch the region R of integration and switch the order of integration. F(x, y) dy dx y 2 2 -4 -2 2…

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Q: d d Calculate r:(t) · r2(t)] and r:(t) × r2(t)] first by differentiating dt dt the product directly…

A: r1(t)=cos(t)i+sin(t)j+3t kr2(t)=2 i+t k

Q: Use any method to simplify the complex fractloh. k+1 25k 3k - 1 15k

A: Use the fraction rule; abcd=a·db·c   The given expression is: k+125k3k-115k

Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function

Q: f(u) = u + u g(x) = cos (x) Find the following function and derivatives. (Express numbers in exact…

A: We have to find out function

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy = -72

A: To evaluate: ∫02∫-72y2∫-48zyz dx dz dy

Q: Consider the following planes. 5x + 2y – z =22 X- 4y + 2z = 0 (a) Find the angle between the two…

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Q: Let R be the region shown in the accompanying figure. Fill in the missing limits of integration. y =…

A: Let's find.

Q: Find the limit. lim (ti – 3j + r² k) 1-2 lim (t i – 3j+r k) = i+ j+ i k %3D i

A: The question can be solved using the concept of limits.

Q: Find the average value of f(x) = v9 – x over the interval (0, 3]. Write the exact answer. fave 1…

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (ë, g) = | (?,?) y = z

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Q: 7x and y = 5x². Sketch the region enclosed by y Decide whether to integrate with respect to x or y.…

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Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = V x2 + y2,…

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Q: Set up the definite integral required to find the area of the region between the graph of y = 18 - z…

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Q: Let f(x) = 10x + ax² + e2×. Compute f()(x). (Use symbolic notation and fractions where needed.)

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Q: If f is continuous at a number, x, then f is differentiable at x. True

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