Using an appropriate substitution, the integral [2 e²+tane sec²0 de is equal to O none of the other choices 2e²+tane + C

Q: Solution:- Given H(jw) -(4+jw) 6+5jw-w² It Can rewrite as:- (jw+4) (- : ; ²= + 1) 6+ (jw)² + 5jw…

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Q: Find the radius of convergence, R, of the series. R = 00 Σ n = 2n(ln(n))² 4n I = X Find the…

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Q: The gradient at (-2,1) is

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Q: By using the substitution t² determine the convergence of = S ∞ dx (x+1)√√x*

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Q: Find the radius of convergence, R, of the series. (x - 10)" Σ n = 1 R = 10 Find the interval, I, of…

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Q: Find the values of p for which the integral converges. (Enter your answer as an inequality.) p>1 8…

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Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: Consider the following. u = -9i2j4k, v = 2j + 2k (a) Find the projection of u onto v. (b) Find the…

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Q: Apply L'Hôpital's Rule to evaluate the following limit. It may be necessary to apply it more than…

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Q: Find the derivative of f(x) = (8x — 9) ƒ'(x) = 10 Simplify as much as possible.

A: f(x)=(8x-9)-107

Q: Find the solution of the given initial value problem: y(4) + 2y""+y" + 8y′ − 12y = 6 sin(t) + 80e¯t;…

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Q: Consider the following equations. f(x) = x5 + 3 g(x) = x + 3

A: Here we have to plot a graph.

Q: A rectangular box with an open top has a length of x feet, a width of y feet, and a height of z…

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Q: ydy 4. S (1 + 3²) ² 4

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Q: If f(x) is differentiable at x = a then f(x) is also continuous at x = a. A True B False

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Q: foo 0 dx e²x

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Q: Exercise 10. A wire of length 28 m is to be cut into two pieces. One of the two pieces is to be made…

A: topic- Application of derivatives

Q: (+²+ 2) y² - 4 ty=4t, y(0) = 3

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Q: Question 9 of 10 Consider the piecewise function f(x), where A is a constarit. >2 where 3 x? as a ad…

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Q: Determine whether the series is convergent or divergent. Σ Στ Σ n = 1 +4

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Q: 5 Plot the point P that has Cantesian Coondinates (x,y) = (4√3,-4) and then polar coordinates (1₁0)…

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Q: 2. Find the curvature of f(x)= x cos²x at x = π

A: The solution is given below

Q: 6. Find the equation of the tangent plane to the surface: ==√√4-x²-2y², at (1,-1, 1)

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Q: Find the derivative of the function. f(x) = arcsin(8x) + arccos(8x)

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Q: Compute the gradient of the following function and evaluate it at the given point P.…

A: Solve the following

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer…

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Q: Use the chain rule to find the indicated partial derivatives. z = x² + x²y₁ x = s + 2t - u, y = stu²…

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Q: 6. Write down the partial differential equations for; (a) Diffusion equation (b) Wave equation,…

A: Diffusion equation identical to heat equation  Wave and Diffusion equation contains partial…

Q: Evaluate e 2 e D dx 2 X (LAX) ²

A: In this question, we want to evaluate the given definite integral.

Q: For the next two exercises, determine whether the integral converges or diverges. f 4 dt sint + √t 5…

A: For (5),…

Q: Determine the principal P that must be invested at rate  r = 3 1 2%,  compounded monthly, so that…

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Q: Find the radius of convergence, R, of the series. (x - 10)" n n = 1 R = 10 Find the interval, I, of…

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Q: A manufacturer knows that when he charges p dollars per unit for his product, he will be able to…

A: Given :Ax=5+x50x=380-20p

Q: How did he get the value inside the circle by ===//= √xlt) sin (nwot) dit bn cl 11 2 (= (₁-7) Sin…

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Q: 2a It costs c dollars each to manufacture and distribute backpacks. If the backpacks sell at x…

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Q: 6³ sin ¹(3x) dx.

A: Solution of given question is written in below steps.

Q: Consider the parabola given by the equation: f(x) = 2x² - 12x Find the following for this parabola…

A: Concept: vertex of the parabola: A parabola's vertex is the location where the curve turns steepest.…

Q: The general solution of xdy - ydx = x²e*dx is A B с D y+xe*+cx=0 x-yex + cx=0 x+yex-cx=0 y−xe*-cx=0

A: We have to solve

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: How did he get the value (jw) ² x 10) = Uw)² x1w) = w2x/m) 1 inside the circle wa) A е (b-a) [ (@jwb…

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Q: dx 2+2 sinx + cos x

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

A: We will apply Ratio-Test

Q: For the equation given below, evaluate y at the point y - 6x² + 24 = 0.

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Q: Why did the sign change from positive to negative?

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Q: Test for convergence or divergence, using one of the tests listed below. Σ(²1-042) n+1 n = converges…

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Q: Find the gradient vector field of f. f(x, y) = xe³xy Vf(x, y) =

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Q: Evaluate the iterated integral below. π T/4 A lago S. 0 1 y cos (x) dy dx

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Q: 1.) Find polar coordinates (r,8) for the point P that has Cartesian coordinates (x, y) = (5,-5) such…

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Q: Given H(jw) -(4+jw) 6+5jw-w² an rewrite as:- (jw+4) -+₁) 6+ (jw)² + 5jw (jw+ 4) (jw+3) (jw+2) (jw+3)…

A: Topic:- application of calculus

Q: Integrate √2 2 | sin x 2 √1-x² dx

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