Find each limit, if it exists. 4- 8x 4x³-5 lim II

Q: Differentiate the following. Do Not Simplify. y=(sin x)(lnx) b) y = (e² + √√cos x) c) y = = a)…

A: To differentiate the following.a y=sin xln xb y=ex+cos x37c y=1-tan x3x3

Q: if / 2³3 rsin rda -x³ cos x + 3x² sin x + 6x cos x Oxsin x O cos x sin x X COS X = 6 ƒ ƒ(x)dx, then…

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Q: Simplify. (x3 · x3)2

A: We know, a. xk.xl=x(k+l) b. (xk)l=xkl

Q: -3. For the function f(x) = -5x - 3, find the slope of the tangent line at x =

A: We can find the slope in the following steps.

Q: Evaluate I se sech¹0d0. 4

A: We have to find out integral

Q: Find the area under the curve y=sin2xcosx for the given limits; sketch the area. Hint: integral in a…

A: Topic:- application of integration

Q: This

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Q: 13. What is the maximum value of the parabola ? 5 0 5 a) y = 3 b) x = 4.9 -Cr- 5 c) y = -1 d) There…

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Q: Find the slope of the tangent line to the curve − 3x² + 2xy − 4y³ at the point (4, 1). - 44

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Q: QUESTION 4 Given the following function, find the values of f (5,2). x f(x,y) = 5 + xln(xy-9) O A.…

A: We can answer the question as below.

Q: S By an appropriate trigonometric substitution, S: I 1 √10 sin 0 cos² Ode Cos 0 10 sin 0 -do |…

A: Here we will use Trignometric sunstitution for given integral.

Q: or the equation, find the slope m and y-intercept (0, b) (when they exist). (If an answer does not…

A: An equation of the form y=mx+c called slope intercept form of line where slope = m and y-intercept =…

Q: A water tower is located x = 275 ft from a building (see the figure). From a window in the building,…

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Q: If fa rsin xd a. -6 b 6312 C. 6 d - 3 2 = -x³ cos x + 3x² sin x + k fx x sin xdx, find k

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Q: help

A: Acute angle are measured from 0 to π/2

Q: Use differentials and the graph off to approximate the following. (Round your answers to three…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) 7 y = 6√x + dy = 3 x 1 1/2 x I 3…

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Q: Explain how the fundamental theorem of calculus relates integrals and derivatives. Formats T B T U…

A: Fundamental theorem of calculus relates integrals and derivatives.

Q: Answer all of the questions below about the function f(x) graphed below when x = 5. 8 8 f -10…

A: Given Graph:-

Q: Use the graph of the function f(x) shown below in order to determine all values of a in the interval…

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Q: Question 14 (1 point) ✔ Saved Determine the scalar equation of a line with a normal vector passes…

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Q: Find dy dx dy if y dx = x³ + 8x + 6 x² - 5

A: Given: y=x3+8x+6x2-5

Q: For the function ƒ(x) = x² – 11, find the equation of the tangent line at å = −12.

A: Given function f(x)=x2-11 We have to find the equation of tangent line at x=-12 Derivative of a…

Q: An internet bookstore charges $15 shipping for orders under $100 but provides free shipping $100 or…

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Q: C. Domain Range D. Domain Range

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Q: -5 -4 -3 -2 -1 5 4 3+ 2+ 1+ -2- -3+ -4 -5+ ܐ 2 3 4 5

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Q: If what does the following integral equal? 4 1₂ 3 h(v)dv= 9 [h(v)dv = 15 - 3 and 9 Ione h(v)dv= = =…

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Q: 12. Determine whether the following is true: (a) ≥3, EZ, 31(2²" - 1); n (n + 1)(2n +1) (b) 12+22+ 32…

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Q: y² = -25x 10- + the equation of the me focus is (Type an ordered pair. Type an integer or a…

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Q: A manufacturer has determined that the total cost C of operating a factory is C = 2x² + 60x + 200,…

A: Firstly we have to solve for average cost per unit as given in the question.  Then apply…

Q: Find the indefinite integral and check the result by differentiation. COS X 1 - cos²x dx

A: Recall; sin2x+cos2x=1

Q: Find the velocity, acceleration, and speed of a particle with position function r(t) = (5 cos t,…

A: Given, r(t)=5 cos t, -3t, 5sin t

Q: A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or…

A: Here is the solution:

Q: If f(x) Files = Time left 0:5 sin²x and g(x) = 1 + cos²x, how are f'(x) and g'(x) related? Maximum…

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Q: State the domain: -8 -6 -4 -2 4- 2- 0 --2- 2 4 6 8

A: Solving the problem by finding the value of the domain of the given graph.

Q: A street light is at the top of a 17 ft tall pole. A woman 6 ft tall walks away from the pole with a…

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Q: Compute the rotated area bounded by y = 2x, x = 2 and x-axis about x-axis

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Q: Find the extrelne values of the function f(x,y)=4x2+ 7y2, on the circle x² + y²=1.

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Q: Explain why the integral is an improper integral and evaluate it: =dx √x-2

A: Given integral:- ∫251x-2dx

Q: A particle moves along the x-axis so that its position at time 0 ≤ t ≤ 18 is given by x(t), whose…

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Q: If 2x² + 3x + xy = 3 and y(3) = — 8, find y' (3) by implicit differentiatio

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Q: (2x² + 2xy + y²) dx + (x² + 2xy - y²) dy = 0

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Q: A point is graphed in rectangular form. Find polar coordinates for the point, with r> 0 and 0 ≤ 0 <…

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Q: The function f(x) has a domain of [-9, 9] and is plotted below such that the porti of the graph on…

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Q: Given that answer= 5 f(x) dx = 3' what is 11 f(w)dw?

A: Property of Integral : 1.∫abf(x)dx=I ⇒ ∫abf(w)dw=I   2.∫abf(x)dx=I ⇒ ∫baf(x)dx=-I

Q: S 3 T 2 For the above rational function f(x)= 3 Q 17 2x² +2.5 . identify the interval on which f is…

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Q: Determine whether the function is differentiable, continuous, both, or neither at the value where…

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Q: 1. Express the following equation in vertex form: y coordinates of the vertex point. 2 = 3x² 12x +…

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Q: Consider the function f(x) x² + 7x + 12 2-5 a. Find the first derivative. f'(x) = b. List any…

A: Solution is here

Q: Find the curvature (t) of the curve r(t) = (−4 sin t) i + (−4 sin t)j + (1 cost) k

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