A. Find the derivatives of the following functions: 1. f(x) = (-x - 5)* 2. f(x) = (-x² - 4)-2

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

A: Given: f(x)=e3x, c=0

Q: Using the figure shown, find sing (3, - 4) -3/5 3/5 4/5 -4/5

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Q: Í sinh(1 - 4x) dx Answer:

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

Q: Solve the following system of equations : 3x - 2y = 18 %3D -x+7y = -44 %3D

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Q: Given f''(x)=7x+6 and f'(−1)=−1 and f(−1)=1.   Find f'(x)=    and find f(3)=

A:

Q: Find the interval of convergence of the power series. (Be sure to include a check for convergence at...

A: The given power series,         ∑n=0∞x2n

Q: The Differentiation to be made must be based on the following topics. - Inverse Trigonometric Give 3...

A: Find your answer below 

Q: Find the area between the curves y = x2 - 8 and y = 4 - x.

A: Explanation of the answer is as follows

Q: S sin?3ß cos11ßdß

A: ∫sin23βcos11βdβ ∫ (1-cos6β)(cos11β)dβ/2 ∫(cos11β)dβ/2 - (cos6β)(cos11β)dβ/2 (sin11β)/22 - ∫(cos17β +...

Q: If a force of 60 lb. acts at an angle of 40 to the horizontal, what is its vertical component? 39 l...

A:

Q: What type of discontinuity is present in the function 3x – 2 if r 2 O The function has a removable ...

A:

Q: Find the indefinite integral. 2+ 4x + 3. dx B+ 6x² + 9x + 2 Step 1 du/dx dx Let u = Begin by rewriti...

A: The given integral,       ∫x2+4x+3x3+6x2+9x+2dx

Q: Set up but do not evaluate, an integral for the length of y = Vr +2,1<r<7 using, 2 dy dx (a) ds = 1+...

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Q: 3. Find from the following functions: dx y = (12x + 2)(7x + 3)3/2 18+2x+7 y = (i) (ii) (3x+6)2/3

A: 3)I) y=(12x+2)(7x+3)3/2 ii)y=(18x2+2x+7)/(3x+6)2/3.

Q: Sketch one possible graph of a function f(x) defined on R that satisfies all the listed conditions. ...

A:

Q: 03) Evaluate the following integrals: A) y = sec(tan-1x). tan³(tan-1x) 1+x2 dx

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Q: Calculate the differential of the following function. Z = 2x³ex? + In(x+y²)

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Q: . Find the arc length of a point that moves with a constant speed of 60 mph along a circle in 15 min...

A: Speed of the point = 60 mph time = 15 min ⇒time t=1560 hr. =14hr.

Q: Compute the angle between the two planes 2x + 3y + 7z = 2 and 4x - 2y + 2z = 4.

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) = In(x), n = 4, c= 3 %3D P4(x) ...

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Q: Let the height of an object bef(t)=t2+2t−4f(t)=t2+2t−4. What is the instantaneous rate of change of...

A: Given query is to find instantaneous rate of change of the object at t = 2.

Q: 3. Let y = cot r + (cot a) In(sin a) and y" Show that -3 cot r +2y. %3D csc² r 4. Given the function...

A: Given: y=cotx+(cotx)ln(sinx)

Q: The derivative of the function y = x(tan-'(3x))² is: y' tan (3x) 6x + (1+9x²) tan-³(3x)] tan (3x)[6x...

A: y = x(tan-(3x))2 dy/dx = (dx/dx)(tan-(3x))2 + x(2(tan-(3x))(3))/((3x)2 +1) dy/dx = tan-(3x))2 + 6x(t...

Q: f(x) Find g'(3) given that f(3) = -6, f'(3) = –4 , and g(x) = %3D %3D 8 Answer:

A:

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

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Q: Use sigma notation to write the Taylor series about x = 4 for the function. 1 x +1 k =

A: This question is based on Taylor series Sigma notation.

Q: ()" e n n=0

A:

Q: Jcos" (3x) sin (3x)dx in' (3x)dr

A: topic - integration 

Q: uestion 1| a) Evaluate the average rate of change for each function over the given interval: i. f(x)...

A: We are authorized to answer one question at a time, since you have not mentioned which question you ...

Q: Given that f(0) = 1, f(1) = 3, f(3) = 55, find the %3D %3D %3D unique polynomial of degree 2 or less...

A:

Q: nd two numbers whose sum is 24 with the condition that the sum of the square of one plus six es the ...

A: Topic:- calculus

Q: 00 Suppose that anis an infinite series with partial sum SN= 7- 10 16 What are the values of anand a...

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Q: Find the derivative of the function y = sin^-1 x/sqrt 1 + x^2 – tan^-1 x. %3D

A:

Q: 1. Find the y" of y = (4x - 3x + 1) (5x + 7) 2. Find y" given y = cosx + sin 3x 3. Find all the deri...

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Q: 2. 조우 X*-xy y-3 Find van d

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Q: sin 0 d0 cos? 0 +5 cos 0 +6

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Q: Find the equation of the parabola y = ax^2 + bx +c that passes through the points (-1,-4) (1,4), and...

A: topic  -  parabola 

Q: The graph below shows the percentage of the parent atoms left vs. the number of half lives that have...

A:

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

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Q: Given f''(x)=−25sin(5x) and f'(0)=−5 and f(0)=1.   Find f(π/4)

A: topic - integration 

Q: Determine whether the following series is convergent or divergent. 1 1+ 1 t.. 22 33 44 O The series ...

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

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Q: Given the following graph, what is the exponential equation that relates the variables?

A: Here x = independent variable y = dependent variable k = y - intercept = ( 4.5 0.1) m/s2

Q: Find the domain of the function H(x)= 2x+3/33-4x

A: The domain of a function is the complete set of possible values of the independent variable

Q: Consider the series E ne-n? n=1 If we let f (x) = xe = re-r2 then S f(x) dx %3D O is finite. O is no...

A: The given series,     ∑n=1∞n e-n2

Q: Diferential equation Pls dont skip steps on the solution  The population of a village grows with a ...

A: Given, The population of a village grows with a ratio proportional to the population at time t. The ...

Q: Q.2\Prove the Maclaurin series: (-1)"-1xn In(1+ x) = En=1' ,-1<x<1.

A: We have to prove maclaurin series.

Q: The Differentiation to be made must be based on the following topics. - Power Rule Give 3 examples w...

A: It is required to give three examples with solution and final answer on differentiation using power ...

Q: The derivative of the function y = x(tan¬1(3x))² is:

A: This question is based on chain rule differentiation.