In each case determine if the Diophantine Equation has a solution. If it does find two solutions. a) 21284x+354756y=68 b) 25704x+249288y=25

Q: Determine whether the series 11n? + 8n + 32 is n³ + 3n2 – 7n + 1 n=1 convergent or divergent. b)…

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Q: Consider the following equations. f(y) = y(7 – y) g(y) = -y Sketch and shade the region bounded by…

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Q: Find the radius of convergence, R, of the series. 00 (x - 9)" "ח n= 1 R = Find the interval, I, of…

A: Use power series concept

Q: Let v=5i+2j. Find a vector that is twice the length and points in the opposite direction as v.

A: This is a problem related to vector. Based on the general formula and concept we will answer the…

Q: 10 Evaluate the summation i. i=1 55 10 1

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Q: Let u = cos(r + y), x = 2st +t and y = t – 2s. Use the chain rule theorem to compute du for du and…

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Q: Determine whether the series is convergent or divergent. If it is convergent, find its sum. (If the…

A: We have to find if the series converges or diverges.

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A: Draw the region and use the washer method of finding the volume of revolution of solids.

Q: Evaluate the following limits if they exicts, show complete solution.

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Q: dx sin x

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Q: Find f. f"(x) = -2 + 18x – 12x?, f(0) = 2, f'(0) = 14 f(x) =

A: Here we will find f(x),

Q: SIXE-A Consider the graph shown to the right 4. lim f(x) X-axis 5. Evaluate lim f(x) X+3" 6. lim…

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Q: Determine whether the infinite geometric series is convergent or divergent. If it is convergent,…

A: Given query is to find series converges or diverges.

Q: Suppose there are 10 points in a plane such that no three points are collinear. How many distinct…

A: We have been provided with 10 points in a plane such that no three points are collinear.We need to…

Q: Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of…

A: Use area concept of integral

Q: 21. A group of 10 women and 6 men must select a four-person committee. How many committees are…

A: Let's find.

Q: 2. Solve for x the equation sin1 3x - cos1 2x = 6

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Q: Find the centroid of the region bounded by y = Vx, y = 0, and x = 9. This region is covered by a…

A: We have to find the coordinates of the centroid.

Q: dy dy if x cos 'y= x+y. Hence find the value of dx if x = 0. dx 4. Find

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Q: 1. Consider the function f(x) =-2(3x– 3)* + 1. a) State transformations. b) Use TWO of the following…

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Q: 9. (Trigonometric Substitution) Let x = 2 sin(0) for 0 < 0 < . Write v4 – x2 as a trigonometric…

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Q: Consider the graph and determine the open intervals on which the function is increasing and on which…

A: Observe the given graph and decide whether function is increasing or decreasing.

Q: What is the slope of the tangent to the curve y=arctan 4x at x= 1/4 A. -2 B. 0 C. 1/2 D. 2…

A: To find the slope of tangent to the given curve.

Q: Solve the following differential equation y"+2y' +y=x-1 Select one: O a. YG.S= Ce¯+c,e¯2x+x-3 O b.…

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Q: 9* 3 19. P. 8" 4 P. 10 7 20. 8* 6

A: 19. P39P4820. 19.

Q: Determine whether the diff eq. is exact. If it is, find the general solution.

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Q: Find the volume of the solid that results when the region enclosed by the given curves y = e-2x, y =…

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Q: Find the Taylor polynomial of order 3 generated by x at a. 1 f(x) -, a = 0 x+6

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Q: How to find point of intersection?

A: You have to sketch the graphs using a graphing calculator like this:

Q: Write 32/3 as an integral

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Q: Solve

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Q: Solve the differential equations: (a) = 4x+2x+5 where V(1) = 10 .

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 1 of 22 Each of the following measurements can be identified as a scalar or a vector. For the…

A: The given data is: For the vector only, which one has the greatest numerical values.

Q: 8. (x'-20) (x-3)

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Q: Consider the function f(t) : 8 sec-(t) – 10t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

A: Topic = Anti derivative

Q: Find all values of x (if any) where the tangent line to the graph of the given equation is…

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Q: Find the nine roots of -256 – j256/3.

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Q: 3x + 1 Consider the function f(x) Compute each of the following. Simplify your answer and use x - 3…

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Q: f(1) . f'lx) dx

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Q: Find the first derivative of the following functions Y = x5 e-3 ln x and Y = ln √ [ (x – 1 ) / ( x…

A: Solution is given below:

Q: Problem 4: Use theorems on limits (limit laws) EXCEPT for the polynomial function rule, to get the…

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Q: Use the Limit Comparison Test to determine the convergence or divergence of the series. 6" + 1 n = 1…

A: Solve the following

Q: Find the general indefinite integral. (Use C for the constant of integration.) sec t (8 sect + 9 tan…

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Q: Create a table of values for the function 9 lim 3 -0.1 -0.01 -0.001 0.001 0.01 0.1 f(x) Use the…

A: Given problem:-

Q: 486 on the interval [8, 20]. Find the absolute extrema for the function on the given interval.…

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Q: At what point on the given curve is the tangent line parallel to the line 3x - y = 3? y = 3 + 2ex –…

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Q: 6. 2y²e»² dx + 2xye»*dy = 0

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Q: 3. Compute f (x)dx f(x) = { 2x if x <1 4 if x 21

A: Given: fx=2x if x&lt;14  if x≥1 And I=∫04fxdx The Power rule: ∫xndx=xn+1n+1+C

Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find a.…

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Q: Answers

A: We will find the derivative using Chain rule.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.