Differentiate the following function. r(1) = (e!2e!-4e) %3D r(1)=

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A: Given ptoblem:- 3. If f(x)=√(x-1), g(x)=√(x+1) find the domains of (fg)(x) and (f/g)(x). Is (fg)(x)…

Q: 3x2 – 2x – 8 - Let f(x) 3x2 – 11x + 6 - This function has: 1) A y-intercept at the point 2)…

A: Simplify the function using definition of asymptote.

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A: From cartesian to polar coordinates we have the following conversion formulax2+y2=r2 i.e.,…

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A: The solution for the question has been provided both on paper and on the graphing tool desmos for…

Q: Which of the following is NOT a differential equation? Select one: x + 2y" = 3 O None. O 2xy' = 3 O…

A: The given problem is solved below.

Q: Which of the following is the particular solution of a nonhomogeneous differential equation…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost the…

Q: 4 Consider the following geometric series: 2 + 8. 16 + ... Identify a and r, find a formula for the…

A: solution:-2+43+89+1627+...first term, a=2common ratio, r=8943=23general term, an=arn…

Q: Problem #2: Differentiate f(x) = [(2x3 – 8)(5x² – 3x – 9)]° and solve f'(2). Solution: Reason:

A: The given function,      f(x)=2x3-85x2-3x-93

Q: Mathematics

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Q: In the following exercises, find each indefinite integral by using appropriate substitutions. dx 8.…

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Q: x2-4 dx S xVx2-9

A: solution:-∫x2-4xx2-9dx=∫xx2-9dx-∫4xx2-9dx                            =12∫2xx2-9dx-4∫1xx2-32dx…

Q: For the differential equation (x² – 4)y" + (x – 2)y' + 2y= 0, the singular points are: %3| x=2 and…

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Q: x-3 Analyze the following limits and find the vertical asymptotes of f(x) = x -9 a. lim f(x) b. lim…

A: The given function,   f(x)=x-3x2-9

Q: 1. Find two sets of polar coordinates for (x, y) = (-V3,1, one with r> 0 and one with r< 0, both…

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Q: The following series 08 2n Σ (-1)" 4n 3n+1 n=1 17 37 converges to converges to 20 the above O the…

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Q: Find the point on the line y = 4x + 3 that is closest to the origin. %3D (x, y) = %3D -

A: Given query is to find the Indicated point .

Q: Find f. f"(t) = 5et + 4 sin t, f(0) = 0, f(1T) = 0 f(t)

A: topic- differential equation

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A: Given :limn→∞ n

Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

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

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Q: Using decomposition into partial fractions, 4x2 + 2 dx x(x2 + 2) is equal to In/x (x² + 2)| + C…

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Q: 8- Consider u=x², v=1/u+1 and w=vv find dv/dx

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Q: 4. Let R be the infinite strip between the x-axis and v= xex x20. Determine if the area of R is…

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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: 00 n2+9 E(-1)"-1 n2+ 8 n=1 a) Show that the ratio test fails b) Test the given series for…

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Q: The exponential function f(x) = e² is the mysterious function c) which is its own derivative. Based…

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Q: Determine if the infinite series is convergent or divergent. State the test that you're using and…

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Q: 5.1. Find the area enclosed by r = V cos(0). (Ignore the r= 2 cos(0) for this part of the problem.)…

A: 5.1) To find the area bounded by the curve r=cosθ

Q: 2. Write the given (total) area as an integral. a. The area above the x – axis and below y = 4 – x²…

A: 2a intersection

Q: Evalute The Line integral of The Fiel f=xi+zj+yK o ver The helix rz cost i +sintjt tK for osts I

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Q: can you say about the series a, in each of the following cases? |an+1 lim n- c0 (a) an absolutely…

A: We have to find the convergent test

Q: a. Find the derivative function f' for the following function f. 5. Find an equation of the line…

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Q: The rate of change of the monthly sales of a new video is given by S'(t) = 500tà and S(0) = 0 where…

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Q: Using two or more complete sentences, explain how to find the sum of the geometric series. n-1 4 n=1

A: Infinite gp

Q: Question 2 ( x? Consider the function f(x) = . x2 -1 (a) Find the intercepts of the graph of f (if…

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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: Using Sandwich Theorem, the sequence 1 cos? n + 1 an = 4 - n converges to 4 converges to 2 diverges…

A: Given

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Q: cos(xy) + secy = 5

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Q: Solving by variation of parameters y"-3y' x the general solution is: O None of them O c_1+c_2…

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Q: evaluate the integral - sin (x) dx (x) 1- sin |3|

A: The given integral,      ∫sin(x)1-sin2(x)dx

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

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Q: 4. State and prove the law of sines in triangles. 5. Prove lim,0 V2r + %3D 6. Figure out the…

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Q: x-3 Analyze the following limits and find the vertical asymptotes of f(x) = x2 -9 a. lim f(x) b. lim…

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Q: Starting with the graph of f(x) = 4", write the equation of the graph that results when: (a) f(x) is…

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Q: Find the absolute maximum and absolute minimum for the given function on the ir f(x) = x3 + 3x² – 9x…

A: Topic:- application of derivatives

Q: The following sequence (7532h n! an = e O diverges converges to e converges to 0 converges to 1

A: Given problem:-