Will the limit of all polynomial functions f (x) as x approaches a be always equal to the value of f (a)? Justify and give examples

Q: Consider the function f(x) = – 4(x – 3)2/3. For this function there are two important open intervals...

A: To find: The value of A which is critical number also need to determine the interval -∞,A,A,∞ at whi...

Q: dx Vitex

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Q: For the following expression indentify the correct form for partial fraction decomposition. x3 + x2 ...

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Q: Let r(x) = f(g(h(x))), where h(1) = 4, g(4) = 5, h'(1) = 5, g'(4) = 3, and f'(5) = 7. Find r'(1). r'...

A: To find out r'(1). 

Q: Question 8 Let f (x) and g(x) be antiderivative of h (x), The which of the following is true? d A -(...

A: Given problem:-

Q: A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certai...

A: We have to find rate of change of the brightness after t days and 5days

Q: Consider the following. 2x3 +5x2-32x-80 x2 x) %3D - 9x + 20 (a) State the domain of the function. al...

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Q: Please only solve 9,12 by partial fraction

A: We need to solve integrals by using partial fraction method.

Q: sec (0) J de 5-sec2(0)

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Q: Evaluate the following indefinite integral. Use C for any constant of integration. 56 dx x2 – 49

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Q: Two solutions to y'' – 6y' + 34y ešt sin(5t), y2 = et cos(5t). = 0 are yı a) Find the Wronskian. %3D...

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Q: x(2x² + 1)°dx

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Q: When you evaluate: ax. The sum of the coefficient of X'' for any constant nis A 16 7 12 7 8. D E Non...

A: Given ∫x3-1xdxExpand:=∫x52-1xdxApply linearity:=∫x5/2dx-∫1xdxWe know that ∫xndx=xn+1n+1=2x7/27-2x

Q: 5. Verify that, for any constant C, y = t+4vt +C satisfies the differential equation (y-t)y' = y-t+8...

A: Given differential equation 

Q: Directions: Please write your solution on the space provided and boxed your final answer. *Introduct...

A: The given function,  f(x)=x2+2x-3x-1if x≠14if x=1

Q: -mpute the average of f(x) = 5a² + 9x on the interval -2, 2].

A: Given query is to find the average of the average value of the function.

Q: Determine whether the series converges using the limit comparison test. 4k2 – 2k + 5 Σ 16k6 + k - 16...

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Q: In a certain city with predictable weather, the temperature (in °F) t hours after 8 am can be modele...

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Q: | cos(Tx)|+ x2 I a+1 + 5x + 137 (9) Find all a so that dr converges. You do not have to find the val...

A: We shall use the limit comparison test to answer this question.

Q: Find the equation of the tangent line to the function f(x) = In(5x) at x = 2. (Use symbolic notation...

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Q: EXAMPLE 3 Find the area of the playing field described by R: - 2 s x S 2, - 1- V4 - x < y<1 + V4 - x...

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Q: (6x+y^2)dx+y(2x-3y)dy=0 solve using exact equations (diff eq)

A: I am attaching image so that you understand each and every step.

Q: QUESTION 4 Write the negation of the sentence-11 s x < 15 (where x is a particular numbe For the too...

A: This question is related to logic. Solve in step .  

Q: (2+7sin 2 dr 3. Co s 2

A: Given: I=∫2+7sin3zcos2zdz We know that the trigonometric identities; 1). sin2θ+cos2θ=12). 1cosθ=secθ...

Q: f(x) = Vr+ 5. (a). Use f'(x)= lim +hD-f(=) to find f') (b). Find the equation of the tangent line fo...

A: Given  f(x)=x+5 a. To find f'(x) using limit definition b. To find equation of tangent line at x = -...

Q: Use the graph of the function f shown to the right to estimate the indicated function values and lim...

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Q: Determine whether the seavence converges dive ges. If it conveges, find the or

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Q: Question 5 Determine the coefficient of Cot(x) when we evaluate [cot(x) – csc(x)]²dx_ 1 (A 2 B 2 Non...

A: ∫cotx-cscx2 dx

Q: 25 and sec 0= 24 25 Determine the values of the trigonometric functions of 0, where csc 0= 7 sin 0 =...

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Q: Problem 3. Use the method of Lagrange multipliers to find the indicated еxtremum. You may assuтe the...

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Q: . The population of the state of Georgia (in thousands) from 1995 (1 = 0) is modeled by the function...

A: NOTE: Refresh your page if you can't see any equations. . for the year 2000, take t=5 ............

Q: A table of values for f, g, f', and g' is given. f(x) g(x) f '(x) g'(x) 1 3 4 6 8 7 7 2 7 9 (a) If h...

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Q: For the next three questions, consider the differential equation: y" - 2y + y = e arctan r 48. If th...

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Q: Evaluate the following improper integral. If it diverges, then type 'DNE. Otherwise, find its exact ...

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Q: Use synthetic division to divide. (Simplify your answer completely.) 180x - x X - 6 x + 6

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Q: 2+X IT X f(x) = 6-x if x20 ... O A. The point(s) of discontinuity is/are x = (Use a comma to separat...

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Q: the line y = 8. y-0 x=1 x = 4 Step 1 The distance from the center of the rectangle to the axis of re...

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Q: A number of matrices are defined as [A] = |1 2 l5 6] [4 3 71 [B] = |1 2 6 l2 0 4] Perform the follow...

A: Note: Since you have posted a question with multiple sub-parts we will solve the first three subpart...

Q: B. Describe the intervals wherein the function is continuous. 1. 2. 10 10 8- 8- 6- 4 2 -10 -8 -6 6. ...

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want...

Q: Evaluate the expression using the given figure to obtain either a or B. 35 -1 (a) tan 12 12 (b) sin ...

A: tan-13512

Q: Assume that it costs a manufacturer approximately C(x) = 1,152,000 + 340x + 0.0005x2 dollars to manu...

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Q: Find csc (-270°). Select the correct choice below and, if necessary, fill in the answer box to compl...

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Q: A pair of dice is rolled. let X be the sum of the number of dots onthe top faces. The table below sh...

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

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Q: Solve the following differential equations of 1- ye** . dy = dx; dy 2-- %3(1+ y*)e* dx m dy x(2lnx+1...

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 00 (-1)*+1 Σ 7...

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Q: Find the solution of the given initial value problem. ty' + 3y = t – t+ 5, y(1) = 3, t > 0 y =

A: ty' +3y=t2-t+5  

Q: The integral of the given function | sin22x cos 7x dx is equal . ....

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Q: Steps are being attached to a deck, as shown in the figure to the right. The bottom of the steps sho...

A: Topic   -  trigonometry 

Q: , Which of the following processes is stationary? A) An MA(1) process with 0 = -1.6 B) Y, = 58.46 + ...

A: The stationary process is