Determine the slope of the tangent line, then find the equation of the tangent line at t = 36. x = √t, y = 5t Slope: Equation:

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A: Two functions f(x) and g(x) are given. We have to draw graph

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Q: For y = xe^(-1/x), find the intervals of increase and decrease.

A: given function To find: the intervals of increase and decrease.

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Q: pлd¹ The rate of flow, Q of a fluid through a pipe of diameter, d and a length, L'is given by Q…

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Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

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Q: Consider a right triangle with a side of length x opposite angle A, a side of length y opposite…

A: we are given that

Q: * Find the general Solution of dy dx = 4. x² ln x

A: The given differential equation is

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Q: A candy box is made from a piece of cardboard that measures 37 by 20 inches. Squares of equal size…

A: Given:A candy box is made from a piece of cardboard that measures 37 by 20 inches. Squares of equal…

Q: f, o x sin(x − y) dxdy = Jo J, x? sin(x − y)dydx

A: ∫−12∫06x2sin⁡(x−y)dxdy=∫06∫−12x2sin⁡(x−y)dydx

Q: Use the following function to answer this question ; f(x)=sqrtx+7, g(x)=2x+4, h(x)=x/2   a/…

A: Use the following function to answer this question ; f(x)=sqrtx+7, g(x)=2x+4, h(x)=x/2

Q: Find the orthogonal trajectories of the family of curves y² = kx³

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Q: Please show steps. Derive the Laplace Transform of the function f(t) = t² (recall that the Laplace…

A: The given function is  To find:-The Laplace Transform of the given function

Q: You are playing on the beach with your dog, Ohana. You throw the ball into the water at a point that…

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Q: Evaluate F. dr along each path. (Hint: If F is conservative, the integration may be easier on an…

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Q: Find all functions f(x) such that 7x f'(x) - and f (0)

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Q: Evaluate the integral by interpreting it in terms of areas. 4 [3₁ |x| dx

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Q: Estimate the area under the graph of f(x) = x² +5 over the interval [0, 10] using 10 approximating…

A: We have given a function f(x)=x2+5We have to estimate the area under the curve in the given interval…

Q: Find the exact coordinates of the centroid of the following semicircular plate. Show all steps…

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Q: Let Find the values of a and b so that f will be differentiable at x = 5. a = b = i √(x) = {2x²+ A…

A: We have been given a piecewise function.. We have to find the values of a and b so that f is…

Q: Evaluate the integral by interpreting it in terms areas. L(7x-14) de Part 1 of 3 We are concerned…

A: The given integral is The function

Q: 6. Given the implicit curve, x² - In line at (1,1). In () = 1, Write the linear approximation L(x)…

A: The given implict equation is

Q: Consider the region bounded by the graphs of x = 0, y = cos(x²), y = sin(x²), and x =

A: Region is bounded by x=0,y=cos⁡(x2),y=sin⁡(x2), and x=π2Rotating the region about y-axis.

Q: Use natural logarithms to solve the equation. -0.417t = 6 The solution is t = 0 (Simplify your…

A: Consider the equation

Q: The graph of a derivative f' (x) is shown in the figure below. LA 1 2 3 4 5 6 -3 Enter the exact…

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Q: Find the work done by the force field F in moving an object from P(-7, 5) to Q(5, 5). 2x. F(x, y) =…

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Q: Use Green's Theorem to evaluate the line integral. S 2xy dx + (x + y) dy C: boundary of the region…

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Q: -2 -1 2+ 1 T 1 y=h(x) 2 True/False True or False: At every point where h'(c) is zero or does not…

A: To determine whether the following statement is true or false.At every point where  is zero or does…

Q: * Find the general Solution of :- - dy хе dxx New 1=Y, NOVIR VO

A: The given equation is; dy/dx = xex

Q: Use power series operations to find the Taylor series at x = 0 for the following function. XCOS TX

A: f(x)=xcos⁡πx

Q: Given u(x, t) = 3e, compute: 4, Uxx =

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Q: 2. Sketch the graph of the quadratic y=- =-2(x+3)² +8 by using a series of transformations. Show all…

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Q: 4. Here is a graph representing a function of the form f(x) = a b*. Find the values of a and b. Show…

A: The exponential function is

Q: for f(x) Verify that the hypotheses of the Mean-Value Theorem are satisfied √49 – x² on the interval…

A: we have given that

Q: Find the slope of the tangent to the curve - cosx- sinxat x-. -2 7/2 1

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Solve the following integration :- 5 (x-3) (x+5) (x-2) dx

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Q: Substitute the expressions from the previous steps. Then substitute (x, y) = (1, 1) and solve for dy…

A: To find the slope of the tangent line to the curve  at the point .

Q: Find u x v, v x u, and v x v. u = 2i + 6k v = 5i + 9j - 2k. (a) -54i + 22j + 18k u x V (b) V x u 54i…

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Q: Let P(t) represent the number of grizzly bears in a population at time t years, when t ≥ 0. The…

A: P(t) is increasing at a rate directly proportional to 600-P(t)P(0)=400

Q: Express the limit as a definite integral. [Hint: Consider f(x) = 8x5.] 72 lim 72+00 1 L' 0 Srdr ²8.…

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Q: Use power series operations to find the Taylor series at x = 0 for the following function. cos²x…

A: Taylor's series.

Q: Q-1: For each of the given equations, first bring all terms to the left side of the equation, then…

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Q: Z 0.68 (0). -0.68 -19.00.00 Drag the surface to rotate 0.68 Drag the surface to rotate t 0.00 .68…

A: From this picture, we can easily get the required traces

Q: Two cars are headed for the intersection of the two roads. If Car A is travelling south at 43 km/h…

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Q: If the marginal revenue for ski gloves is R'(x): = -0.7x + 40 and R(0) = 0, find the revenue…

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Q: Find the area of the surface over the given region. Use a computer algebra system to verify your…

A: I have appended the formula used in the solution procedure

Q: Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints…

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Q: The vector field F(x, y) = (-y sin(xy), -x sin(xy)) is the gradient vector field of the function…

A: find r(t) at t=2,t=0

Q: 10. An electric scooter manufacturer estimates that the cost C (in dollars) of producing x scooters…

A: Given, Where C is the cost of producing x scooters in dollars  We have to find the production level,…