С. O c. v = 2 m/s

Q: Question 3 1-. a) [. following series -): : Determine whether the (-1)"4"-1 32n+1n n=1 is convergent…

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Q: The integral 4x dx Vx2 – 4 1 is an improper integral of typel is an improper integral of type II…

A: The given problem is solved below in detail.

Q: Activity 1. Match the functions in Column A with their corresponding antiderivatives in Column B.…

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Q: Using appropriate substitution, [sec (2x) + 1] tan(2x) dx is equal to

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Q: Without evaluating the constants, the partial fraction decomposition for 5x² – 3 f(x) (x³ – 4x²)(x²…

A: We have to solve partial fraction.

Q: Exercise 1. Find the following limits 2 3x + tan 2x 2x + x tan 2x sin 1) lim 2) lim 5x +x tan 2x 3)…

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Q: Find the curvature of the space curve. r(t) = - 3i + (3+2t)j + (t +8)k %3D

A: The given curve    r(t)=-3i+3+2tj+t2+8k

Q: Part a: Assume that the height of your cylinder is 4 inches. Consider A as a function of r, so we…

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

Q: The graphs of the first and second derivatives of a function y = f (x) are given below. According to…

A: Solve the following

Q: Find the angle between the given vectors. Round to the nearest tenth of a degree. u- 2j, v = 9i - 4j…

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Q: . The population of a town reaches 113000. 7 years ago the population was 82000. Assuming that the…

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Q: 4. 7. Suppose f(x)dx = -6, f(x)dx 6, and g(x)dx = 2. Evaluate the following integrals. 2 ... Jgndx =…

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Q: Evaluate 3 x2 - 2y ds where C is the line segment from (3,6)to(1,-1)is C Non of the above -58.240…

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Q: O A- 32°, B - 59°, C = 89° %3D

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Q: Find the first five terms of the Taylor series for the function f(x) = lnx) about the point a = 2.…

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Q: If In a + In(x- 5) = In(2x), then x = Show your work on paper. Use the space below to upload a…

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Q: Express the series using sigma notation 6m + 3m + 0 + (-3m) + (-6m) ...

A: Consider the series 6m + 3m + 0 + (-3m) + (-6m) ...

Q: dx Vx+2

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Q: Find the domain and range of y = log,(7 + 5x). The domain is: The range is : > Next Question

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Q: A differentiable function f(x, y) has the property that f(1, 4) = 5 and f-(1, 4) = 3 and f,(1, 4) =…

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Q: + NR6. An exponential function can be written in the form y = a(c)* +kwhere the equation of the…

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Q: 6 Find the sum of the arithmetic series, 3n+2. 50 75 100 25 O O O

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Q: Given f(x,y, z) = In(x² + y² + z²), show that ² f , ²f , ² f x² + y2 + z2

A: Given problem:-

Q: 6 What is the recursive formula for the sequence 3, -12, 48, -192, 768,...? a 1 = 3, a n = (a n -…

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Q: Use the figure to find the exact value of the trigonometric function. Find cos 20. 29 21 20 41 841…

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Q: The solution of the ordinary differential equation -y(4) + 4y" = 0 is: O c_0+c_1 x+c_2 e^(3x)+c_3…

A: Given -y(4)+4y''=0To find solution of Ordinary Differential equation:

Q: Consider the parabola given by the equation: f(x) = 4x° – 10x + 2 Find the following for this…

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Q: 4 Which of the following is the correct expansion of (3x - 3y)2? 9 x2 - 18 xy + 9 y2 9 x2 - 9 y2 9…

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Q: 10 8 Consider the function f(æ) Let F(x) be the antiderivative of f(x) with F(1) = 0. Then F(x) :

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Q: 2. Find the volume of tetraherdon with the vertices A(-1, 2,0), B(0,3,-1), C(3,3,0), and D(1,1,-1).…

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Q: Which of the following is the particular solution of the differential equation dy = e ;y = 1, when x…

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Q: 3- A box with an open top is to be constructed from a square piece of cardboard, 3m wide , by…

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Q: Nathan invested $2,870 for 219 days at a simple interest rate of 2.75% p.a. How much more or less…

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Q: 9- Find the coordinates of the absolute maximum an d minimum points for f(x)=2x²-x* given x €[0,4] :

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Q: compute J, f(x)dx 2x if x < 1 f(x) = { 4 if x2 1

A: Given query is to find the value of the integral.

Q: What is the coefficient of the second term in a binomial that is raised to the sixth power? 5 15 20…

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Q: Solve the given equation for x. 420-4 = 39 You may enter the exact value or round to 4 decimal…

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Q: Which of the following statements is true about the function f whose derivative is f'(x) = (x -…

A: Given that f'(x)=x-12x+2

Q: Evaluate the summation i=1 28 10 30

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Q: - Find the point of tangency and the equation of the tangent line passing through the point p(-4,-2)…

A: Given: Now, f'(x)=-3-2x. At (-4, -2), slope = -3-2(-4) = 5. So, the equation of the tangent line is…

Q: a. Use the Intermediate Value Theorem to show that the following equation has a solution on the…

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Q: x-3 3. Find lim and simplify. x+9 x-9

A: Solution

Q: A radius r of a spherical balloon is increasing at a rate of 2 cm/s. Find the rate of a volume V…

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Q: ()6 = K 3- 0- 0. 3 6.

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Q: Compute the partial derivatives: ,2 z = In(x² + y³) az dy

A: Use partial derivative

Q: Given the geometric sequence where a, = 2 and r = 2 Find a10-. 32 256/2 32/2 256 O O

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Q: The solution y, of the homogeneous differential equation y() + 36y" = 0 is O None of them c_1+c_2…

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Q: The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of…

A: Explained below

Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² – c² and y = c² – x² is…

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Q: 12. Let y = 4x-4x+3. %3D (a) Find the equation of the tangent line to the graph of the function at…

A: Solve the following