45-74. Definite integrals Use a change of variables or Table 5.6 to evaluate the following definite integrals. 1518 1 45. 46.. cos 2x dx 2e²x dx

Q: Consider the following function. g(x) = (x - 2)²-9 Step 3 of 4: Find two points on the graph of the…

A: Consider the function

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. 4n²+3…

A: The given series By Root Test If L<1 then series convergent If L>1 then series divergent If…

Q: 9. Find the interval of convergence of the series: 2¹ (x + 3)¹ In(n) ∞ n=2

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Q: 8. Evaluate the definite integral. a. 6 e² + 18 e² + 18z dz

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find y'. y = y'' = 16 tan (4x + 1)

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Q: Vs = ft - f- f+ + f =

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Q: 2 Assume that f'(2) = -9, g'(3) = g(3)=2, and y=f(g(x)). What is y' at x = 3?

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Q: Given that ß = 101°, y = 24°, c = 15. Which of the following equations solves for a? a) a = (15 sin…

A: Given that the triangle we have to find choose the correct option

Q: 256x The volume of a sphere is increasing at a rate of 3 cm³/sec. Find the rate of change of its…

A: The expression for the surface area of the sphere is:Where r is the radius of the sphere.The…

Q: 9.5 4.5 9.5 » [*¨* f(x)dx = 6, [^¹³ f(x)dx = 3, [ f(a)da = 3, [ f(x)dx = 8. 2 (Section 4.4) Suppose…

A: Find the integral 6f(x)-3, limit from 7 to 4.5.

Q: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph…

A: The objective of this question is to understand the graph of the function f(x) = 5 + 2e^(-0.1x) and…

Q: 2. For f(x)=√14-2x (a). find the domain. Write your answer in interval notation. (b). Graph f(x)=√14…

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Q: Given the definitions of f(x) and g(x) below, find the value of (fog)(-1). f(x)= x +5 g(x) = 2x² +…

A: The given function is .The aim is to find the .

Q: A firm's marginal cost function is MC(q) = 5q¹ + 4q + 10. Find the total cost function if the fixed…

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Q: Evaluate the limit, use L'Hospital's Rule when possible. limx→0 5x In(x+2) O-5 01/2 0 5 Not Possible

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Q: The sales of a new high-tech itern (in thousands) are given by S-104-8003 where t represents time in…

A: The rate of change is equal to derivative of function given.So at first we would differentiate S(t),…

Q: d. y = 2x+1 x²-4 5x+1 e. y = 2√x-1 f. y = sin x ln x-1 x²+1/

A: To find the derivative of the following functions.

Q: Determine the integral by making the appropriate substitution. 1 1+ 4e dx

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Q: Given the function f(x)=x-7, find the net signed area between f(x) and the x-axis over the interval…

A: Given that the function y=x-7 we have to find the area of the region [-1,9]

Q: for Integrals Find or approximate all points a which the given function equals its average value on…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Test the series for convergence or divergence. 72 = 1 (-6)m+1 48m

A: To test the following series for convergence or divergence.

Q: 1. Find the area bounded by x = y²; x = −2y² +3

A: To find the area bounded by

Q: g(t) = t³+ t².

A: g(t)=t3+t2

Q: Find a power series representation for the function. ( ) = n( 11 + y )

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Q: Use l'Hôpital's rule to find the limit. Use -∞o or ∞o when appropriate. 3x²+5 lim x→∞04x³ +2 Select…

A: The objective of this question is to find the limit of the expression (3x²+5)/(4x³ +2) as x…

Q: Question Find the average rate of change of the function in the graph shown below between x = -1 and…

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Q: 2. For f(x)=√14-2x (a). find the domain. Write your answer in interval notation. (b). Graph…

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Q: 13. If there are initially 2000 bacteria in a culture, and the number of bacteria double cach hour,…

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Q: S 3 6x²4x³ dx 24

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Q: Solve the following Initial Value Problem. dy dt - y= sec² (t) + 3 sin(t), y() = 1

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Q: sinh(x) = 314

A: sinh⁡(x)=34sinh⁡x=12(ex−e−x)

Q: Find the area of the region bounded by: p2 = 72 cos 2

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Q: A= B n ed Use the right triangle and the given information to solve the triangle. a=1, c= 8; find b,…

A: Given,

Q: Evaluate [xy dx + (x + y)dy along the curve y = x² from ( − 1,1) to (2,4). C S xy dx + (x + y)dy = C…

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: (b) Use Desmos to graph the surface area function on the following coordinate system. Label each…

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Q: Is the series ∑(1/(n + (1/n))), from n = 1 to infinity, comparable to the series ∑(1/(2n)) using…

A: Solution is following in explanation step.

Q: how that the function is increasing on the given open interval. (Enter your answers as a…

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Q: Find the points on the graph of the polar equation where the tangent line is horizontal or vertical.…

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Q: Evaluate the integral by making an appropriate change of variables. JJ₂² 7 cos(3 (y + x)) dA where R…

A: The given integral  where R is the trapezoidal region with vertices

Q: 6. 14 ) Consider both geometric series below. 3 SA = 00 Σ n=1 5n and SB = M8 n=0 3 5n Both SA and SB…

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Q: Since, the only critical number in the interval [0, 5] is 2, test the values of f(x) at this number…

A: The objective of the question is to find the values of the function f(x) at the critical number and…

Q: ate and classify all (by classifying the extrema, we mean listing whether locate any stationary…

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Q: Find all exact solutions on the interval 0 < 0 < 360°. If there is more than one answer, enter them…

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Q: Evaluate the definite integral. 5 J 1+162 -dx

A: To evaluate the following integral.Note: Since you have posted multiple questions, we will provide…

Q: Question Find the area A of the region that is bounded between the curve f(x) = -2 sin () - 3 and…

A: To find the area A of the region that is bounded between the curve  over the interval .

Q: Find the indefinite integral. [(e² + +6) dx = +C

A: We have to find the integration of

Q: DRAW THE GRAPH OF A FUNCTION WHERE limr-a f(x) DOES NOT EXIST FOR SOME INTEGER a. EXPLAIN WHY THE…

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Q: Find all exact solutions on the interval [0, 27). If there is more than one answer, enter them as a…

A: The given equation is; 9cos(2t)=9cos2(t) -2, [0,2pi)

Q: 31. 3 1-25x2 dx

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS. EXPLAIN YOUR WORK FOR BETTER…

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