cos(x) dx 2) Calculate the integral sinc √sin(x)

Q: Find the general anti derivative of the function f(x)=8x^9-3x^6+12x^3

A: Given,.

Q: Express the limit as a definite integral on the given interval. lim Σ 2x₁² + (x₁") ² Ax, [4, 5] i =…

A: The given limit is

Q: The rate at which a machine operator's efficiency, E (expressed as a percentage), changes with…

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Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = sin²(x) = cos(2x), 0≤x≤…

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Q: 5. Determine the volume of the solid obtained by rotating the region bounded by z = ³ - 5y² and the…

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Q: Using the following solve the following conversion:  16 liters = how many quarts? 1 liter = 1000ml…

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Q: Find the general Solution of :- - dy dx = 3 Sin 2x Cos 2X

A: The given differential equation is

Q: An equilateral triangular plate with sides 10 m is submerged vertically in water so that the base is…

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

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Q: :) = yzi + xzj + xyk _: r₁(t) = ti + 2j + tk, 0 ≤ t ≤ 4 _: r₂(t) = t²¡ + tj + t²k, 0≤t≤2

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Q: B Find the Taylor polynomials p4 and p5 centered at a = 6 for f(x) = 4 cos (x).

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Q: II. Differentials Recall, the DERIVATIVE values represent SLOPE values on a given function. Slope =…

A: A derivative of a function is a representation of the rate of change of one variable in relation to…

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

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Q: 7. Find lim to talk A. 1 C. -1 B. 0 D. does not exist

A: We have to evaluate the limit.

Q: Do the following. (Round your answers to four decimal places.) (a) Estimate the area under the graph…

A: I have appended the formula used below

Q: Find the equation of the tangent line to y = (x³ + 2x + 3) eª at the point where x=0. The equation…

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Q: A 10-foot ladder leans against the side of a wall forming an angle with the ground. Given that the…

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Q: A. f(x): = Match the common function with its Maclaurin series. 1 1 x B. f(x) = (1+x)" C. f(x) = cos…

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Q: Question 4 Find the expression for the exact area of the surface obtained by rotating the curve…

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Q: Congratulations! your answer is correct (and saved). Check Answer/Save Step-By-Step Example Find…

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Q: Question 4.21) Evaluate the following limits. sin² (1)-1 A) lim 1->8/2 1-4 B) lim x-0 1-cos(2x) x²…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: To find the slope of the tangent we need to find dy/dxThen find dy/dx at t=pi

Q: Each of the regions A, B, and C bounded by the graph off and the x-axis has area 3. Find the value…

A: Each of the regions A, B, and C bounded by the graph of and the x-axis has area 3.To find the value…

Q: The graphs of the polar equations r₁ = cos(20) and r₂ = sin(9) + 1 are shown below. Find the 4…

A: We have to find the value of  at which r1 and r2 are equal to 0 and intersection points.

Q: 2. In poker, a straight flush is five cards in sequence that are all the same suit. For example, A,…

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Q: A forest fire covers 2015 acres at time t = 0. The fire is growing at a rate of 8√t acres per hour,…

A: The fire is growing at a rate of 8t acres per hour, where t is in hours.

Q: Suppose f is differentiable and f' is increasing on an interval (a, b) (that is, f is concave-up…

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Q: Solve the following integration :- S. X-3 2 X²³² x ² −X +1 dx

A: To solve the following integration.

Q: f(7) = 18 and n: S 0. f'(0) de = [² 10 0 f(y) dy = -10

A: f(7)=18 and ∫07f(y)dy=−10I=∫07θ⋅f′(θ)dθUsing Integration by Parts∫udv=uv−∫vdv

Q: Consider the curve 5x² - 3xy + 3y³ = 768. (a) Find an expression for y'. y' = (b) P(12,-2) is on…

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Q: You turn to the next task that you were assigned, where an object is moving at a constant speed of 3…

A: Given that an object is moving at a constant speed of  meters per seconds

Q: a) The rectangles in the graph below illustrate a The value of this Riemann sum is left endpoint…

A: given function

Q: The integral √x dx evaluates to

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Q: Given (t)=4sinti+at+4 costi find the arc length for t € [0,*]. What is the formula for arc length in…

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Q: B) y(x) = 2+x

A: I have appended the formula used in solution procedure

Q: Does the sequence San} converge or diverge ? Find the limit if the sequence is convergent. (n+4…

A: The given sequence  nth term is

Q: Tutorial Exercise Express the limit as a definite integral on the given interval. lim Σvil (2 + x)…

A: The definite integral  can be written in the limit form on the interval [a,b] as

Q: Let g(x) = x³ – 6x + 8. Find f(x) so that f'(x) = g'(x) and ƒ(1) = 1. NOTE: Enter the exact answer.…

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Q: Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by f at a. f(x) = 2 In (x), a = 1

A: A Taylor series is given by f(x)=∑k=0∞f(k)(a)k!(x−a)k

Q: Express the limit as a definite integral. [Hint: Consider f(x) = 8x5.] 72 lim 72+00 1 L' 0 Srdr ²8.…

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Q: Using the graph below, sketch the graph of the function y = - f(x). -6 6 6

A: We have given the graph of f(x).The graph of the function y=-f(x) is the mirror image of the graph…

Q: Find the area of the region bounded by the graphs of y = e³y=e-³, x=-4, and x = 5 using integration.…

A: The given function is .The aim is to find the area of the region.

Q: Tutorial Exercise Evaluate the integral by interpreting it in terms of areas. f (x-14) de Part 1 of…

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Q: Determine whether I 5Mm Converges or diverges. If 6 7m m=2 Converges, find its sum

A: Geometric Series∑n=1∞a⋅rn−1 Converges if and only if −1<r<1∑n=1∞a⋅rn−1=a1−r

Q: Find the sum of the series: n=0 (-1)"36¹-2 n!

A: ∑n=0∞(−1)n36n−2n!

Q: n's Theorem to evaluate the line integral (y - x) dx + (2x - y) dy C wen path. : boundary of the…

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Q: IN Now look carefully at the function. What is the actual value of y when x-1?

A: We need use inspection method for the given graph to find the value of y at

Q: Substitute the expressions from the previous steps. Then substitute (x, y) = (1, 1) and solve for dy…

A: To find the slope of the tangent line to the curve  at the point .

Q: For the given function, find all values of c over the interval (3, 10) stipulated by Rolle's Theorem…

A: f(x)=x+2x-1, (1/5,10)

Q: Approximate the area of the region bounded by the graph of f(t) = cos (t/2 - 3/8) and the t-axis on…

A: given funciton