3 x2 dx 4

Q: Find the nth Maclaurin polynomial for the function. f(x) = eX, n= 5 Ps(x) = ||

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Q: 2. Find the indicated limits of the following algebraic and trigonometric functions: x' -1 а. lim. -...

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Q: у %3D Зx5 — 15x4 + 20х3 + 3 -

A: Given : y=3x5-15x4+20x3+3   To Find : x & y- intercept of the given graph

Q: X = cos 2t, y = cos t, 0 <t<T

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Q: 6 du dx. Transforming the integrand, the result will be k , where k is a constant. What is u and k? ...

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Q: Given: JV5x² - 3 xdx. If we let u= 5x - 3, which of the following u-substitution formula is applicab...

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Q: Suppose f(x) - 6'Vi+ť' dt. 1) Evaluate / (2).

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Q: Calculate F. dS where F = (3xy°, xe", zª) S is the surface of the solid bounded by the cylinder y? +...

A: Let's find. 

Q: O : (2r-3)/ar- 12x²+ 7 – 2 im |2x*-3 + Vart- 12r²4 7|} +C V4r4– 12r2+7|}

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Q: Question 9 5x2 tan( 3x) dr. ifu=3x*, then the resulting integral is SFlu) du. Find Given: A 18 none ...

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Q: Write the first five terms of the sequence, give the exact answer: +00 n+ 19 n=1 Determine whether t...

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Q: x2+ Consider dx. (x8 + 8x³ + 16x²) 2 Using u-substitution and transformation of integrand, then the ...

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Q: Consider (x8+ 8x5+ 16x2) ² -dx. Using u-sub

A: Given: - The integral is, ∫x2+1xxx8+8x5+16x22dx To find: - The values of k and n. By using u-substit...

Q: Differentiate the functions. 3 a) f(x) = 1– 5x + b) f(x) = (x³ + 4)² %3D

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Q: 7 1 Calculate the following limit. Let an = Vn + In (n) and bn Vn (Give an exact answer. Use symboli...

A: Let's find. 

Q: Let F = Use Stokes' Theorem to evaluate F. dī, where C is the triangle with vertices (9,0,0), (0,9,...

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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: 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: Direction: Compute the following limits: Given: 1 lim f(x) =5, lim g(x) = -9, lim h(x) = 6 1. lim(5 ...

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Q: Given: / 5x2 tan(3x³) dx. Ifu=3x°, then the resulting integral is Jf(u) A B none of the choices 5 18...

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Q: 8-2x (f) lim- X-4 x -x-12 Vx² +16 –4 lim- (g) x' +8 lim x-2 x+2 (h)

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Q: + 0o Consider the improper integral dx. What will be an appropriate solution and answer? x2+ 2x+2 A ...

A: We have to find value of given improper Integral.

Q: 5. Find the centroid of the solid formed by revolving the area between the curves: y? = x and y = 2 ...

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Q: Solve the equations: 8х - 2у - 13 -2x +5y- 8.

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Q: When you perform polynomial long division on the rational expression a²+3x+3 the numerator of the re...

A: The rational expression,    x2+3x+3x+1

Q: 5. Find the centroid of the solid formed by revolving the area between the curves: y2 = x and y = 2 ...

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Q: 3. Evalnate. the. following.double.intagrals.by.comverting to Polar.Caa.r.dinates. 2 2 Anse. T(e-1) ...

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Q: Inz Let U = ry ,x= Vst, y = s? - 1². Use the chain rule to find when s = 1, as 4. -. t = 2.

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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: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say ...

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Q: 6. Consider -dx. Transforming the integrand, the result will be k , where k is a constant. What is u...

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Q: Suppose f(x) = "6r V1+f dt.

A: Topic = Integration

Q: + oo Consider the improper integral dx . What will be an appropriate solution and answer? x2+ 2x+ 2 ...

A: We have to find solution of improper integral.

Q: topic: calculus of polar curves 1. Find the slope of the curve r = 2cos 4Ɵ 2. Find the slope of th...

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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: Classify the series as absolutely convergent, conditionally convergent, or divergent. (-1)*+1k! (2k ...

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Q: Using the definition of derivative, find functions: a) y = xVx -2 .2 (b) y =- (x-1)

A: Given ,f(x)=xx2-2Therefore,f(x+h)=(x+h)(x+h)2-2We know that ,f'(x)=limh→0f(x+h)-f(x)hTherefore,f'(x)...

Q: 1 Use the Cauchy's integral test to show that Σ diverges n. In n. In In n n=2

A: Cauchy -Integral  Test series ∑n=1∞ an      converges if integral ∫1∞ f(x) dx finite and  diverge if...

Q: Do the following: (a) Construct the table of values; (b) graph the function; and (c) find the indica...

A: Since you have posted multiple questions in this question which are not interlinked so I have solved...

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

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Q: Find the distance between the points (distance formula) 1.(3, 2), (4, -3)

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Q: x'- 36 lim 16 x+6 (a) Vx+11-4 lim- (b) х -5 (c) lim- +2 2-x

A: Since the student has posted many sub-parts of the question and does not mention any specific part, ...

Q: Determine whether the given series converges or diverge E3n°4-n n=1

A: solution:-∑n=1∞3n34-n an=3n34-n an+1=3n+134-n+1 Ratio testL=limn→∞an+1an=limn→∞3n+134-n+1 3n34-n =li...

Q: tan (In |4x2|) -dx is b in cos (In |(2x)*|)|+c. The integral of What is b?

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Q: Explain briefly why the function f(x) = e" – x³ – 8 eIntermediate Value Theorem. Use IVT to show tha...

A: We will use the Intermediate value theorem. 

Q: The differential equation x*(x – 2)²y" + 3(x – 2)y' + y = 0, as the singular points at x = 0 and x =...

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Q: Determine whether the series converges. k=1

A: We use limit test to find convergence or divergence of given series. Follow 2nd step.

Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) = (1 + x)4 Σ f(x) n = ...

A: Explanation of the answer is as follows

Q: Differentiate the functions by using product or quotient rule. a) f(x) = (1 – 3x?)• e Зx+1 b) f(x) 2...

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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...