II. Determine the derivative of the ff. logarithmic functions 7. y = 12x² log 8x 8. y = In 25x %3D 5x3

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

A: Explanation of the answer is as follows

Q: Find the nth Maclaurin polynomial for the function. 2x – 5 - f(x) n = 4 %3D X + 1 P(x) = %3D

A: According to question,Given Function,fx = 2x-5x+1n = 4

Q: 2. Use the Intermediate Value Theorem to show that 2.x - 3 if – 3 0 has a zero on the interval [-2, ...

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Q: A consumer has utility function xy u(x, y) = x+y

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Q: Calculate F . dS where F = (4x°z, 4y°z, 3z*) S is the surface of the solid bounded by the hemisphere...

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Q: Use the difference a -a, to show that the given sequence (a,] is strictly increasing or strictly dec...

A: The given sequence is; {an} = n/(3n-2).

Q: 3x -dx be given. If 4=e*+2. then the resulting integral is f(u) du.compute f (3). e* +2 Let 2 (A 3 B...

A: We have to find value of f(3)

Q: Find the nth Maclaurin polynomial for the function. f(x) = e¯X, n = 5 Ps(x) = %3D MastarIt

A: Given

Q: Question 15 Evaluate the integral V4x 4x4 12x2 +7 xdx. (4x* – 12r?+7) /2 +C 24 B(2x-3)/4x4- 12x2+7 +...

A:

Q: Solve the components of the given equation of conic sections and sketch the graph а. х — -y2 +1 b. x...

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Q: O g(x) = (3t+ 2) dl t %3D

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Q: Use the formula for the binomial series: (1 + x)" = 1+mx+ + 21 = 1+ £in to obtain the Maclaurin seri...

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Q: 1. J sec x csсх 2. S sin*x dx 3. S e2*(Vx + 1) dx

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Q: If the solution to e2x sec2(e2x+1)dx is equal to k tan (e2x+1) + C, find the exact value of k. 1 A 2...

A: This question can be solved using the concept of integration by substitution.

Q: Use the limit comparison test to determine whether the series converges 8. 74 +5 The series Save for...

A:

Q: entences. 5k + 7k +1 3k* +8k? +9 -). az

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: a. Show by means of slope that the four points (0,0), (-2,1), (3,4), and (5,3) are vertices of a par...

A: This is a problem related to geometry. For parallelogram opposite sides are parallel to each other. ...

Q: A region is enclosed by x = y² and x = k , where k is a positive constant. The area of the region be...

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Q: 1. What is (3x) ? 2. What is (x*+ x)? 3. What is (2-32)? 4. What is (6v - 3v + Sv)? 5. What is (x-1)...

A: As per the guidelines we can solve 3 parts only 

Q: Situation 3: Find the area enclosed by the graph of the curve x^2+8y^2+16 = 0, the x-axis, the y-axi...

A: according to our guidelines we can answer only three subparts, or rest can be reposted.

Q: Express the repeating decimal as a fraction. 0.4713 43 43 43...

A: In this question we have to express the repeating decimal as a fraction.

Q: Find the Maclaurin polynomials of orders n = 0,1, 2, 3, and 4 and then find the nth Maclaurin polyno...

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Q: /4x+ – 12x² +7 xdx . Evaluate the integral A) -(4x4 – 12r²+7)/2 +c 24 © ! (21--3)/- 121+7 – 2 m 21--...

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Q: State whether the following integral is Convergent or Divergent. e*dx 8. O Convergent O Divergent

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Q: 3. a) Find the percentage error in computing u = Vx at x = 2.45, when x is 4 %3D b) | If Ax = 0.005,...

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Q: a b d - b -1 Use the fact that if A = , then A c d = 12 and A 'A=12. to find the inverse of the give...

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Q: 2. Find the equation of the tangent line to the curve at the given point by eliminating the paramete...

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Q: cot (2x) dx . V cot2(2x) – 15 Evaluate the integral csc (2x) -Arcsec 4 A +C 4 O - - In [cor (2r) + V...

A: This question can be solved using the concept of integration by substitution and some special integr...

Q: 5x? tan( 3x³) dx. fu= 3x³, then the resulting integral is f(u) du. Find A Given: 4 A none of the cho...

A: Topic:- application of integration

Q: 14 n+3 n+2, n=1

A:    ∑n=14n+3n+2Compute the sum of an=n+3n+2 for n=1…4=43+54+65+76=9920

Q: Find the radius of convergence and the interval of convergence. 00 k(k + 1) k=1 1) First apply the R...

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Q: 3. Find dx dy d²y and y 1+t and if x = %3D dx2 1+t

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Q: 1g graph, clearly showinng any pointS where the graph crosses the nate axes: + 7x + 10r

A: We will draw the graph. 

Q: /atch the video on the improper integral 1/x^2 2 and the video on the nproper integral 1/x 2 before ...

A: We use the formula integration of ex dx=ex.

Q: The curve C with equation y = f(x) passes through the point (1, -3). Given the following, find f(x) ...

A: We know, ∫xndx= x(n+1)/(n+1)

Q: A company that manufactures small canoes has a fixed cost of $20,000. It costs $100 to produce each ...

A: Follow the procedure given below.

Q: Find the nth Maclaurin polynomial for the function. 4x - 1 f(x) : n = 4 x + 1 Pa(x) =

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Q: The function f is defined by the following rule. f(x) = 2* Find f(x) for each x-value in the table. ...

A: Find inverse of L. Let x=L(t) 

Q: d?y Find dr2 for the functlon: .3 3x +4x y=x

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Q: Write out the form of the partial fraction decomposition of the function (as in this example). Do no...

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Q: f(x) =(x^2/3 − 1)^2 Take note that the 2/3 is the exponent if x (a.) the critical numbers of f (b....

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Q: A. Evaluate the following integrals 1. 2. L. 3. , e*dx dx dx -1 x2/3 4. SE tanodo -4 dx

A: solution:-Q.(4) ∫-∞π2tanθdθsolving the improper integral=limt→-∞∫tπ2tanθdθ=limt→-∞∫tπ2sinθcosθdθ=lim...

Q: Evaluate the following limits using L'Hôpital's rule   2. lim x→0+ tanh x/sechx − 1

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Q: x + px+6, x22 (b) Functions f(x)={ x-2, x<2 (4– 2x, x22 and g(x)={ are 9-x, x<2 continuous at x= 2. ...

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Q: f(x)= (x-2)/(x^2-x+1)^2 (a.) the critical numbers of f (b.) all relative extrema of f (c.) the inte...

A: To find (a.) the critical numbers of f(b.) all relative extrema of f(c.) the intervals on which f is...

Q: Name: Section: Find the derivative of the following. Show your solutions. 1. What is (3x) ? 2. What ...

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Q: Determine whether the series converges. k=1

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Q: Determine whether the series converges, and if so find exactly its sum. Otherwise type none in the b...

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Q: Question 2 du where u= {(x) and for some constant, k. Compute /\2). The integral reduces to e + 1 A ...

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Q: uestion 9 x2 dx. Which of the following options is correct? 00 onsider 9+x6 (A Arctan 3 + lim Arctan...

A: