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

A: We need to find the Taylor Series of e5x with center c=0.

Q: cot (2x) Evaluate the integral - * xp- V cor (2x) - 15 csc (2x) (A) -Arcsec +C 4 (B -- In cot (2x) +...

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

A: f(x) = 16 ln(1+x)f0(0) =16 ln(1)f0(0) =0f1(x) =f'(x)=16x+1f1(0)=16f2(x) =f''(x)=-16(x+1)2f2(0)=-16f3...

Q: Sow) du. #glu)- u+1 Using u-substitution, the integral reduces to a new integral evaluate the new in...

A: Topic:- integration

Q: Find the solution of the following Differential Equations 2) (xdy – ydx)/x² = 4) 2.x In(y)dx+ yx'dy ...

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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: r2+b2 (b) Using suitable differentiation laws, find if y = (where a, be R). (c) The parametric equat...

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Q: Let F = %3D So Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of the ...

A: Here, the given function is F=xy,5z,4y To use Stroke's theorem: ∫CF·dr=∫∫S∇×F·N^ dA And, ∇×F=ijk∂∂x∂...

Q: Consider dx. Which of the following options is correct? 9+x6 1. lim Arcsin lim Arcsin 6. 6. 3 B none...

A: Given

Q: Prove that the following statement is true for all positive integers. 1 1 1 + + 4 8 1 2" – 1 + 2n Pn...

A: Given; Pn : 1/2 + 1/4 +1/8 +...+1/2n =(2n -1)/2n

Q: One model for the spread of a rumor is that the rate of spread is proportional to the product of the...

A: Let's find. 

Q: Question 13 Consider the integral dx. Using u-substitution, what is the appropriate u and du? 2e 3e2...

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Q: x²+ Consider dx. Using u-substitution and transformation of integrand, then the power formula (x*+ 8...

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Q: State whether the following series is Convergent or Divergent. n=1 O Convergent O Divergent iM:

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Q: Compute P,(f,0)(x) for the following function: f(0) = 42, f"(0) = 23, f) (0) =19, f®)(0) = 17, f("(0...

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Q: 1. Consider the relation R1: R2 - R such that (r1, y1)R1 (x2, y2) if and only if both points are on ...

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Q: a tivb where a, b and c are integers and Solve the following equation, glving the complex roots in t...

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Q: 3. Suppose that z = f(x, y) is a differentiable function with respect to variables !! x and y and is...

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Q: Use the ratio test for absolute convergence to determine whether the series converges or diverges. I...

A: Ratio Test :  Suppose ∑ak be an series and            ρ = limk→∞ ak+1ak , then(i)  If ρ <1 , then...

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: The following diagram shows a sketch of a curve with equation y = f(x). The points A(-3, 0), B(0, 0)...

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Q: x² - 36 lim X6 x+6 (a) Vx+11-4 lim (b) x-5 (c) lim- x2 2-x x +6x+9 lim (d) r+3

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Q: x³dx (v²– 1)7 3.

A: In this question we have to find the value of Integration.

Q: Is the series divergent or convergent? Show solution and explanation. +oo In n E(-1)": n2 n=2

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Q: Find the general term of the sequence, starting with n = 1, determine whether the sequence converges...

A: Given sequence is GP. and ntg term of gp is an =arn-1

Q: dx Given: 7-ge-2x. Using u-substitution and transforming the integrand, find du. A 18e-2xdx B - 18e-...

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 00 k+1 Σ (2k –...

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Q: Find the products AB and BA to determine whether B is the multiplicative inverse of A. -32 4-1 A = B...

A: A=-32-44  ,  B=4-11-1AB=-32-44 ×4-11 -1AB=-12+2     3-2-16+4     4-4AB=[-10  1-120]

Q: Use any method to determine whether the series converges or diverges. (k!)° (9k)! O The series diver...

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Q: sin 3x Given: -dx What is the appropriate formula to find the integral? cos? (3x) (4-3 sec 3x) du (A...

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

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Q: A trapezoid has an area of 36 sq. m and an altitude of 2m. Its two bases have ratio of 4:5. Find the...

A: A trapezoid has an area of 36 m2 and an altitude of 2 m. Its two bases have ratio of 4:5. Let, a=4x...

Q: dx The integral can be re-written as (A) (2-2 V1-m ) lim m- 00 B none of the choices lim (-2+2 /1-m ...

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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: f(x) =(x^2/3 − 1)^2 -Take note that the 2/3 is the exponent of x -please answer sub part c,d,and e...

A: According to question,Given Function,fx= x23 -12

Q: Find the tangent plane of the surface z = f(x, y) at (0,0, 0) in which 3y f(2, y) = || cos /3 t dt.

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Q: 4. y = 2 -10x 5. y = 88 8x + 888 6. y = 2021 7×^6

A: According to our company's guidelines I can only answer first three subparts of the question since y...

Q: 2) Find the tangent to the curve y 2 tan at x 1.

A: A detailed solution is given below.

Q: Watch the video on partial fractions decomposition with linear factors before answering the question...

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Q: f(x) =(x^2/3 − 1)^2 -Take note that the 2/3 is the exponent of x (c.) the intervals on which f is ...

A: Given problem:- f(x) =(x2/3 − 1)2   (c.) the intervals on which f is increasing or decreasing (d.) t...

Q: An agriculturist wanted to plant seven different organic crops in a small field. To properly study t...

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Q: Given 2 cot- (esc) if – 3 3. a. Determine if f is continuous or discontinuous at r = 0 and at r = 3...

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Q: (a) With the use of a suitable limit, find the first differential of Vr² +b² with respect to r i.e. ...

A: topic - derivative using first principle

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: 3(1+x²)-1/2, y(C

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Q: x²dx 1. J4 –x*

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Q: 5x² tan( 3x³) dx. If u= 3x³, then the resulting integral is Jf(u) du. Find . 5/2 A 18 5/2 18 5 18 D ...

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Q: Find the radius of convergence of the power series. (If you need to use oo or -co, enter INFINITY or...

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Q: x' - 36 lim 6 x+6 Vx+11-4 lim x-5 lim- 2 2-x x² +6x+9

A: