8. Calculate the following limits. In z lim → 2²-1 (b) [ 1³-1³ 0 e + cos2-1-2 lim

Q: thats a natural log of 9 to 0 and integral from 9 to e^x

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Q: Problem 2.3 Evaluate 2x² + 3x + 1 2x - 3 lim x-1 x².

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Q: Write an equation for the function f(x) shown. The leading coefficient is 1.  Asymptotes: y=-1 x=…

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Q: Consider the following differential equation to be solved by variation of parameters. y" + y =…

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Q: 4. (x²-5x+6)y" - 3xy' - y = 0; Xo = 0

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Q: a. b. algal dy dx dy dx + y = xy³ - y = ex y² -X

A: See this solution in below.

Q: Explain why the integral is improper. 100 1 10 X 1.4 converges diverges 1.2 1 y 0.8- 0.6 dx 0.4 0.2…

A: To find the value of an improper integral, convert the integral in terms of limits. If the resulting…

Q: Approximate the definite integral using the Trapezoidal Rule and Simpson's Rule. Compare these…

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Q: A force of 660 newtons stretches a spring 3 meters. A mass of 55 kilograms is attached to the end of…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = X, (1, 7, 7) 10 5…

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Q: Vf(1, 3) =

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Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z =…

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Q: 2. Determine whether or not the series converges. State clearly the test you use, and show all…

A: We have to check the convergence

Q: 4 n=n? + 2n 1 4. Σ -(x-3)"

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Q: Find the volume of the solid generated by revolving the region bounded by the curve y = In x, the…

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Q: Find the exact value of the function. √7 3' В tan given tan ß= E 2₁ with 180° <B<270° В 2 (Type an…

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Q: Find the derivative of the function using Chain Rule. h(x) = (2x-6)-¹ (x²+3)

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Q: 10. (a) Construct the Taylor polynomial p3(x) of degree 3 for the function f(x) = 1/(2-x) around x =…

A: Solution is given below:

Q: Find the derivative of the following function. f(x) = sinh 16x

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Q: Solve the given differential equation. x²y" + 13xy' + 36y = 0 y(x) = ,X>0

A: The given differential equation is;  x2y''+13xy'+36y=0.

Q: Problem 2.4 Evaluate lim (√²+x-=-) x X

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Q: Consider these three examples: A. S 1dx 1+x² B. f sin²x C.S.sin x dx We want to solve one using a…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: √2 cos x csc x=2 cos x

A: 2cosxcscx=2cosx

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In√√x² + y2, (3,…

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Q: Evaluate the following integral: Sºa dx -00x²+1

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Q: 1 Give the antiderivatives of

A: The given function 1x2 we have to find its antiderivative

Q: Evaluate the following integral: dx -27 x2/3

A: Solve the following

Q: Evaluate the following integral: Stan x sec³ x dx

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Q: Find the derivative of the function using Chain Rule. (2x-6)-¹ (x²+3) h(x)=

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Q: 4. S 1 x²√√x²+4 dx

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Find the orthogonal trajectory for the family of circles with center at (-2,3) and draw the…

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Q: Problem 2.5 Evaluate lim x →0+ 1 (-/-)

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Q: It is estimated that between the hours of noon and 7:00 PM, the speed of a highway traffic flowing…

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Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

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Q: What is the original price of P1,743,759 discounted price at 22% discount?  (whole number)

A: discounted price = 1,743,759  discount rate = 22%  find original price = ?  this discounted price is…

Q: Find the extreme values of the function and where they occur. 7x X + 1 y= 2 OA. The minimum value is…

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Q: Suppose that in solving an equation over the interval [0,360°), you reach the step sin 0= --- 2…

A: Solve the following

Q: Cut out squares (of the same size) from the four corners of a square cardboard of given side length…

A: The side of the square = L  let the length of the square = x,

Q: Find the gradient of the function at the given poin In(x² - y) -2, (3,8) X Vz(3, 8) = Z =

A: We are asked to find the gradient of the function.

Q: Consider the following differential equation to be solved by the method of undetermined…

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Q: Find f if f"(x)= e-sin z - 3 4√ f'(0) = 0, and f(0) = 8.

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Q: tan12/1-tan^2 12 simplify

A: Simplify tan121-tan212

Q: Find all values of x and y such that Px(x,y) = 0 and Py(x,y) = 0 simultaneously. P(x,y) = 5x²2 -…

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Q: Which of the following graphs is the correct plot of y=- 2 cos(x)? -5+ 3 2 -1 -3 -5 -3 -2 --2 -3…

A: Please see the below picture for detailed solution.

Q: x, evaluate each expression.

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Q: A swimming pool whose volume is 10,000 gal contains water that is 0.03% chlorine. Starting at t=0,…

A: Given: the volume of swimming pool = 10000 gal that contains 0.03% chlorine. at t=0  ,0.002%…

Q: Let R be the region below the curve y = 4x², to the left of above the x-axis. Find the centroid of…

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Q: Estimate the area under the graph of f(x)=1/(x+3) Over the interval (-2,1) using 8 approximating…

A: Given question:- Estimate the area under the graph of f(x)=1/(x+3) Over the interval (-2,1) using 8…