Let f(x) = /20 – x. Compute f'(4) using the limit definition f'(4) - - Find an equation of the tangent line at a = 4 y =

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A: Given query is to find that function is continuous or not at given point.

Q: Determine the diameter of a closed cylindrical tank having a volume of 11.3 m to obtain a minimum su...

A: The volume of the closed cylindrical tank is 11.3 m3  

Q: Use the limit process to find the area of the region between the graph of the function and the x-axi...

A: here we can see that the  graph is between 2 to 4 so the first column graph is right  but from equat...

Q: Nhich of the following p-series are divergent? 00 ロと-4 S ロEsk-品 Σ 6666 10000 k38 ロと-7 1 k=7 ロEk 1000...

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Q: Describe the solid represented by the integral. That is, clearly identifying any functions, bounded ...

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Q: Given the following matrices, perform the indicated matrix operation. 1 7 8 [5 1 2 -2 -4 A = 3 -6 -9...

A: To perform the indicated operation for the given matrices.  

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

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Q: 8. For the function y = e* + sinx: a. Determine y', y",y",y^),y(5), y(6). b. Describe the pattern ob...

A: We have to find the differentiations of the give function and find y101.

Q: Find the area enclosed by the curves y=sin(x), y=cos⁡(x), and the two vertical lines x=0 and x=π/2

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Q: Let's consider the marginal cost function C' (x) = 0.02x + 28, where x represents the level of produ...

A: Given c'(x)= -0.02x+28

Q: Use the alternative form of the dot product to find u · v. ||u|| = 35, ||v|| = 45, and the angle bet...

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Q: 14 Approximate (x - 5) dx using 4 rectangles. It is approximatiey. (If necessary, round to two decim...

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Q: Find the directional derivative of the function at P in the direction of v. h(x, у, 2) %3D хуz, Р(2,...

A: The objective of the question is calculate the directional derivative of the given function.

Q: Evaluate the integral. 2V3 dx 4 V 16 – x2

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Q: Use the arc length formula to find the length of the curve y = 36 - x2, 0 s x S 6. Check your answer...

A: y=36-x2   , 0≤x≤6let f(x)=36-x2  Then  Arc length =∫061+(f'(x))2dx                                  ...

Q: Use mathematical induction to show that: 1 2 + 2 2 + 3 2 + ⋯ + ? 2 = (?(?+1)(2?+1)) 6

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Q: Find the antiderivative of the function f(x) = x*. That is, find a function F(x) for which F' (x) = ...

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Q: 1. Evaluate the following integrals: g) . dx sin-1 x V1 – x2 h) . 2 cos(sec-1x) dx 2/V3 xVx² – 1

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Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflect...

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Q: Test the series for convergence or divergence. TT 17. 2 (-1)" sin - n=1 n

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Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of int...

A: The integral is ∫4+1t31t2dt

Q: The integral of the given function f- (9- dr Arcsin +C b.+ Arcsin + C c. -- Arcsin +c d. None of the...

A: To find the value of a given integral we use the substitution method 

Q: A 13 ft ladder is leaning against a house. The ladder slides down the wall at a rate of 3ft/min. a) ...

A: We have to use differentiation to solve the problem

Q: (3k + 8)! Consider the series> ar k3k k-1 k-1 a) What is ak+1? ak+1 = aktl ? b) What is ak ak-1/ak =...

A: The given series,     ∑k=1∞ak=∑k=1∞3k+8!k3k

Q: y = 10 - 5x, y= 0, x= 0; about x = -1 Need Help? Read It

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Q: The number of bacteria in a culture is increasing according to the law of exponential growth. The in...

A: N(t) =N0 ekt  ...(1)N0 =260N(1)=260 ekN(8)=260 ek8N(8) =2 N(1)260 ek8 =2*260 eke8k =2 eke7k =27k = l...

Q: Find a polynomial of degreen that has the given zero. (There are many correct answers.) Zero Degree ...

A: Given query is to find the the polynomial of the degree three and zero at 9.

Q: Consider the function 1 1- x4 Write a partial sum for the power series which represents this functio...

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Q: _1. Which is the process of using implicit differentiation? A. Derive with respect to x, derive with...

A: Given: Which is the process of using implicit differentiation?  

Q: 9 checik whether the following statemects are true or False. lif En an is conditionally convergent, ...

A: For (i), Let us take an=(-1)nn. So, the series ∑n=1∞an is conditionally convergent but ∑n=1∞an is di...

Q: 16. а — - (V3, 1), ь %3 (0, 5) b = (0, 5)

A: Given query is to find the angle between the Indicated vector.

Q: Determine the extreme values of the function (exact coordinate(s) f(x) = 2sinx – x on the interval x...

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Q: A boy is selling lemonade throughout the hot summer. Suppose the number of cups sold is given by the...

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Q: PROBLEM [ B6 (b) ] : Solve the first order dy = 9 x²e=³, by using dx differential equation Variable ...

A: We have to solve the first order differential equation dydx=9x2e-y by using variable seperable metho...

Q: 1 2 3x2

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Q: Find the slope-intercept form of the equation of the line that has the given slope m and passes thro...

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Q: te ove (2y – x) dx dy 16-y2 12. -4

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Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of int...

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Q: (x2 – x + 1)y = 4(1 – 2x)y O y = (z? - a + 1)* + C O y = C(x? - a + 1)-4 O y = C(x² – x + 1)4 O Iny ...

A: We know, ∫ dx/x = ln|x| + C , C is a constant. ln(a)+ ln(b)= ln(ab) b*ln(a)= ln(a)b  

Q: - 4q° + 700g , where R(q) is in dollars and q Suppose a product's revenue function is given by R(q) ...

A: The revenue function is given by Rq = -4q2+700q Formula Used: MR62 = dRdqq=62 To evaluate: The margi...

Q: A table of values for f(x), g(x), f'(x), and g'(x) has been given. Ax) g(x) f'(x) | g'(x) 3 2 -5 1 2...

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Q: Find (i) the undirected distance between point A and b, and (ii) the midpoint of the line segment AB...

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Q: Evaluate the definite integral. Use a graphing utility to verify your result. 9. OShow My Work (Opti...

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Q: d’y dx² 5 + 6y = 3x+3 dx

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Q: Ted the of eae hee an t a

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Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of int...

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Q: Problem : Find the derivative of the series 16x4 2x 4x2 8x3 32x5 f(x) = 1+ Also 1! 2! 3! 4! 5! show ...

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Q: 1 Value of 1 1+x 1 is: 1+y

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Q: k- 32k 6k+4 Consider the series ak k-1 a) What is ak+1? ak-1= ak+1? b) What is ak ak-1/a ak+1 c) Com...

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Q: Choose the most appropriate answer: Evaluate the integral : f 7x6 dx x7+2 O In(x7+2) + C O In(x7+ 2)...

A: We will use substitution method to solve the integral.