Consider the parametric equations: x = 2t2, y =t³. Find at the point t = dx? 8 without eliminating the parameter.

Q: sin 2n Determine whether the sequence defined by a, %3D 9n converges or diverges. If it converges,…

A: We have to find limit

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Q: A. Evaluate the following integrals: Sx² e**dx 1.

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Q: 5x dV, where E =    (x, y, z) | 0 ≤ y ≤ 2, 0 ≤ x ≤  sqrt4-y^2, 0 ≤ z ≤ 6y   evaluate triple…

A: Answer is 60

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Q: The vertices of quadrilateral ABCD are given as A(0, 3, 5). B(3, – 1, 17), C(7, –3, 15), and D(4, 1,…

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Q: b. Consider the graph of function f below. 1,5) (7,9) (-1,-1) (4.2) (1,-1) Complete the following…

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Q: Determine whether Rolle's Theorem applies to the following function on the given interval. If so,…

A: rolls theorem

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A: Solution of question is written in below steps.

Q: x = r° +1, y=r² -t a) Find dy/dx Show all your work.

A: x =f(t)dxdt=f'(t)   y=g(t)dydt=g'(t)Then,dydx=dydtdxdt =g'(t)f'(t)

Q: clearly

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A: Given query is to find indicated limit.

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Q: 1.82 Let E CR be any unbounded set. Find an open cover of E that has no finite subcover. Prove that…

A: We will proceed as follows

Q: Consider the following function. (If an answer does not exist, enter DNE.) -6 f(x) = 1+ x2 (a) Find…

A: The given function,   f(x)=-61+x2

Q: Find the second-order partial derivatives of the function. Show that the mixed partial derivatives…

A: We need to find partial derivatives.

Q: PROBLEM SET NO. 3 Using the techniques of integration, evaluate the following integrals by applying…

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Q: For the function f(x) = - e, find f'"(x), f''(0), f'"(9), and f"(-8). ... f"(x) =(Type an exact…

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Q: Answer 1 only. Upvote if it is typewritten.

A: We have to find the integral

Q: 1. Below you are given the graph of the function y=(1). Use the graph to answer the questions. a)…

A: Given the graph of the function y = f(x)  i.e. as we put the value of x in function we get value of…

Q: 1. Bob, Glen, and Paul (the authors of our text) are sitting around enjoying their nice, cold…

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Q: The Shatzkins are adding a sunroom to their house. They want the sunroom to have area 14.00 m'. One…

A: Here, they want the sunroom to have the area 14 m2. And, one wall of the sunroom will be part of…

Q: [1+cot 2(In x2)]* dx

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Q: Find by implicit differentation; Dthat the tangent to the eclipse x =1 at %3D Point (TorYo) is LoX…

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Q: Consider the following. u = x w = Vx y = xx Calculate the following. Simplify your answers. du dx dw…

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Q: INTEGRATION OF TRIGONOMETRIC FUNCTIONS AND ITS TRANSFORMATIONS Evaluate the given integrals. Please…

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Q: A. Evaluate the following integrals: 3 | tan°x dx 1.

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Q: 3. Find the extreme values of the function y = x3 – 2x + 4 and where they occur 2

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Q: An Olympic athlete set a world record of 9.65 s in the 100-m dash. Did his speed ever exceed 37 km /…

A: Given : Time =9.65 s Distance =100m

Q: dx 4. S x²+4x+13

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Q: Find the derivative of the function. 4 f(x) x In(x) f'(x) %D

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Q: Which integral has the largest value? a ed f (x) dx f (x) dx f (x) dx f (x) dx

A: We have to find out the largest area

Q: Simplify cos2θ*(1+tan2θ)

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Q: Use the first derivative test to determine the location of each local extremum and the value of the…

A: For given function  f ( x ) = 2 * x * e-5*x we have to find local extremum and it's functional value…

Q: Write the equation for a sphere centered at the point ( – 1, 7, 6) and the point ( – 7, 7, – 5) is…

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Q: Direction: Prove using the three conditions of continuity if the following function is continuous or…

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Q: Find the following limit. x + 2 lim x→-8- x + 8

A: Given that a limit problem and we solve this problem by using general property of limit.       Here…

Q: The function f(x) = x^3 + bx^2 + c has a critical point at (-2, 6). Determine the value of b and c.

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Q: x =r +1, y=r -1 c) Find an equation of the tangent to the curve at the point corresponding to t = 1.…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i+ 4 sin(t)j+ tk;…

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Q: 4. When the graphs of two functions intersect the angle of intersection is defined as the angle…

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Q: If A = 3 B = | J, c = ; ) II. [X1 X21 [x3 X4]' And X= Solve each of the following equations: 1. (d)…

A: Here we have to use the matrix operations.

Q: Let F be the function whose graph is shown below. Evaluate each of the following expressions. (If a…

A: A limit limx→a f(x) exists at x=a if limx→a+ f(x)=limx→a- f(x)=L and limx→a f(x)=L.

Q: If the following series converges, compute its sum. Otherwise, enter oo if it diverges to infinity,…

A: Find your answer below

Q: x =r +1, y=r -t b) Find d'y dx2

A: x = t3+1differntiating w.r.t. variable t;dxdt=3t2+0dxdt=3t2   ....(1)y = t2-tdifferentiating w.r.t…

Q: 6. Find the volume of the solid generated when the area of the region between the curves y = Vsinx,…

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Q: Consider the following cost function. a. Find the average cost and marginal cost functions. b.…

A: Given query is to find average cost and marginal cost.

Q: A factory is dumping pollutants into a river at a rate given by dx/dt = 3/4/100 tons per week, where…

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Q: 2ydx = 3xdy

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Q: dy You need not expand your answer. dx Calculate y = (7x0.5 – x2)2

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