Let f(2)=√4z² + 6z Determine the derivative of f. f'(z) =

Q: Evaluate the integral. S sin (22x) cos (13x)dx sin (22x) cos (13x)dx=

A: To evaluate the following integral.

Q: distance of a moving car in terms of its speed is s = 0.21v + 0.00636v², where s is measured in…

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Q: 3 3x (p²³+ p² - 512+3) y = è +4e²"

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Q: Given f(x) = 5x + 3 and g(x) = x² - 4. Find the composition fog(x)

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Q: 1 Estimate the area under the graph of f(x) = x+2 rectangles. Round your answers to four decimal…

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

Q: Apply the alternating series test to discuss convergence or divergence of the given series. Σ(−1)n+1…

A: 0\\ &2. a_{n+1} \leq a_n, \text{ for all n}\\ &3. \lim _{n \rightarrow \infty} a_n=0\\…

Q: 35. a(t) 36 g(t) = cos 2t; v(0) = 5; s(0) = 7 2t

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Q: At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing…

A: At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/hand ship B is sailing…

Q: f(x) = 12x - x² from x = 0 to x = 6; 2 subintervals a) Approximate the area under the curve over the…

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Q: Find the Taylor polynomial T3(x) for the function f centered at the number a. f(x) = xe-7x, T3(x) =…

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Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. πχ 9…

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Q: Find the centroid of the thin plate bounded by the graphs of g(x)=x² and f(x) = -x + 6. Use the…

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Q: = present in 450 years? A) 32 grams B) 10 grams C) 4 grams D) 1 gram

A: Initial quantity of the substance = 64 gramsTime elapsed = 450 yearsHalf time of the substance = 75…

Q: Find the Taylor series for f(x) = ln(x) about a=2. Find the interval of convergence.

A: Taylor series of ln⁡(x) around a=2A Taylor series is given by f(x)=∑k=0∞f(k)(a)k!(x−a)k

Q: The graph of the function h is shown. m 2.5 fy 2 1.5 1 0.5 0 -0.5 -1 -1.5 -25 Why is lim h(x)…

A: Graph of h(x)

Q: Find the interval and radius of convergence of the following power series. 1. Σx-1 (−1)” 2″ x” n=1…

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

Q: Find the open interval(s) of f (x), graph given below, where f'(x) is negative.

A: We need to find interval notation where f'(x) is negative.

Q: Find the exact length of the polar curve Length = r=3 sin (0), 0≤0 ≤ π/3.

A: To find the exact length of the polar curve.

Q: ,11 h(x) = x¹¹ arcsec(x).

A: h(x)=x11arcsec⁡(x)h′(x)=ddx[x11sec−1⁡(x)]Product Ruleddx[f(x)g(x)]=f(x)g′(x)+g(x)f′(x)

Q: Find a power series for the function, centered at c. 8x x² + 6x - 7 g(x) = g(x) 00 Σ n = 0 = c=0…

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Q: 1. The graph of f is shown to the right. The function F(x) is defined by F(x) = f(t) dt for 0 ≤ a ≤…

A: Given that the function F(x) is defined as The figure

Q: Adding a vector to the zero vector O a) preserves the non-zero vector O b) reduces the vector's…

A: The zero vector isSuppose we have a vector asOn adding the vector with the zero vector we get

Q: Use implicit differentiation to find dy/dx and then d²y/dx². Write the solutions in terms of x and y…

A: According to our bartleby expert guidelines only first three subparts are to be answered kindly…

Q: f(x) = 3x5 f'(x) = 2 이집

A: Given that the function

Q: The polynomial C(t) = -0.006t4 +0.140t³ -0.53t² +1.79t measures the concentration of a dye in the…

A: C(t)=−0.006t4+0.140t3−0.53t2+1.79t

Q: Find the Maclaurin series for f(x) = e-²x. Find the interval of convergence.

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

A: Region is bounded by x=1−y4,x=0Rotating the region about x=61−y4=0y=−1,1Using the washer method

Q: (j) Evaluate the following line integrals, where C is given (i) fcds where C: x = t³, y = t¹,1 ≤t≤4

A: Consider the line integral

Q: 2. Consider the curve y = sinx - on the inteval 0 ≤ x ≤ π/2. (a) Sketch the curve and shade in the…

A: (2)The curve is given as, on

Q: Let F(z) = ™* sin(6t²) dt. S Find the MacLaurin polynomial of degree 7 for F(x). 2x3 -x7 36 7 Use…

A: F(x)=

Q: Question 什 -10-9-8 -7 -6 Find lim f(x) given the graph of f (x) shown above. X-2 Select the correct…

A: From given graph

Q: b(x) = √√√x Answer O 21 2√2|x| t(x) = 2x

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Q: How far did you travel according to your odometer? How far did you travel according to your three…

A: The objective of the question is to determine the distance traveled according to the odometer and…

Q: +x-2xy) ds once around the circle x² + y² = 4, z = 0

A: ∮C(2+x−2xy)ds once around the circle x2+y2=4,z=0x2+y2=4Using parametric…

Q: Question The graph of f(x) is given below. Select all of the true statements about the continuity of…

A: we say a function f(x) is continuous at x=a if the limit of f(x) at x=a is equal to f(a) that is…

Q: Let f(x) = x³, and compute the Riemann sum of f over the interval [6, 7], choosing the…

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

Q: Find two numbers whose sum is 9 and whose product is a maximum. The two numbers are (Simplify your…

A: The objective of this question is to find two numbers whose sum is 9 and whose product is a maximum.…

Q: 60-63. Equivalent constant velocity Consider the following velocity functions. In each case,…

A: Question no. (61):To find the equivalent constant velocity.

Q: Find T5(x): Taylor polynomial of degree 5 of the function f(x)=cos(x) at a=0. T5(x)=   Using the…

A: The given function is  The Taylor series of function y=f(x) at

Q: The function g, which is periodic but not necessarily sinusoidal, has an amplitude of 5 and a period…

A: We have given a function g which is periodic but not necessarily sinusoidal, has anamplitude A=5…

Q: Use the alternative curvature formula k = following parameterized curve. r(t) = (4 + 2t²,2t,0) K=…

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Q: Use the Ratio Test or the Root Test to determine the values of x for which the series converges.…

A: The Ratio TestFor the Ratio Test, we consider the limit:L=limn→∞|an+1an|Where an is the nth term of…

Q: π cos(0) 13) Calculate: 3√1-sin 0 π 3 de

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Q: Write the exponential equation as a logarithmic equation. e0.75 = 2.1170...

A: The objective of the question is to convert the given exponential equation into a logarithmic…

Q: 2) Calculate: a) lim- √x-3-1 x²-16

A: We rationalize the numerator and use the formula (a+b)(a–b) = a2–b2.

Q: Consider the graph of the function f (x) below. Which of the following is the closest approximation…

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Q: X Find the first four nonzero terms of the Taylor series for the function 1+ The first four nonzero…

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Q: D ▶Region D is bounded by y=x² and y=x. Draw the region. Set up the integral xdA in two different…

A: Region D is bounded by . To draw the region. To set up the integral in two different ways: in the…

Q: (b) dy dx = 23 x² +1

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Q: The function f is defined by f(x)= 2 √x x³ - for x > 0. Part A: Find f'(x). Part B: Write an…

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