1. Using the definition, find the derivative of f (x) = x² – 8x + 9 at the number x = a.

Q: Complete the differentiation formulas a) d/dx(c)= b) d/dx(ax+b)= c) d/dx(x^n)= d) d/dx(1/x)= d)...

A: We have to find derivative

Q: Find the volume of the solid obtained by rotating the region enclosed by the curves f(x)=x2+8f(x)=x2...

A: Given problem:- Find the volume of the solid obtained by rotating the region enclosed by the curves ...

Q: If f(x) 3. find f'(4).

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Q: 7. Find the arc length of each curve (integrate by hand) a) x = -8y– 3 on [– 2,6] b) y = , 3 on [0,6...

A: Here we have to find the arc length of the given curves.

Q: x = 3.61 E-6 (A) What is the equivalent decimal number? O-3.61 0.000361 O0.0000361 O0.00000361 (B) R...

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Q: Find the indicated derivative. 11) Find y " if y = 3x sin x. A) y " =- 3x sin x C) y" = - 6 cos x +3...

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Q: -21 Evaluate the integral: rV + 81 (A) Which trig substitution is correct for this integral? Or = 9 ...

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Q: If f(r) and g(x) are differentiable and y = horizontal tangent line at z f(r) has an x-intercept at ...

A: We have to choose correct one.

Q: Igure 3 below shows the region W bounded by the curve y x? and the line y = x. y dd or cre (6,6) rk ...

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Q: 2. Consider the function h(x) = 11 - + x3 a) Find the equation of the tangent line to the graph of h...

A: We will find the equation of tangent line as shown below

Q: (axy-ay) dx +( 3x'y - 4x) dy = 0

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Q: For the functions f(x)=-10x+7 construct and simplify the difference quotient f(x+h)−f(x) \ h The di...

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Q: Find (f -1)(-2) for f(x)=3x+8. Round your answer to two decimals.

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Q: If is the diameter of the circle with A = (-2,6) and B = (5, 4), then the center of the circle is at...

A: AB is the diameter of the circle with A=-2,6 and B=5,4

Q: Compute the directional derivative in the direction of v at the given point. S(x, y) = xy' – x, v=i-...

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Q: Find the derivative with respect to x of f(x) = 2(x + 5)* + 3(x + 5)° + (x + 5)² + 4.

A: The given function, f(x)=2x+54+3x+53+x+52+4

Q: Geometry What is the length of the edge of a cube if, after a slice 1-inch thick is cut from one sid...

A: We have to find the length of one side.

Q: 5. Using an Elliptic Paraboloid as a Reflector. Instead of being used as a receiver like a satellite...

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Q: Find the horizontal asymptote(s) of the function p(z) f (x) Va(z) where p (x) = 3x? – æ – 2 and q (x...

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Q: Which of the following is equal to cos x- sin' x ? 4 | O sin 2x O - sin 2x | O - cos 2x

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Q: 1. Find the volume of the solid obtained by rotating the area in the first quadrant bounded by y = T...

A: Given that y=x2, x=0, y=2-xaround the line x=1find the volume 

Q: Let f(x) 11 In(x). Then f'(x) is andf (8) is f"(2) is and f(8) is

A: Use differentiation for finding the values 

Q: Suppose we have a velocity function and an initial condition for position: 1 1 2t v (t) = r (1) = (0...

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other...

Q: At what point do the curves r (t) = (t, 2 – t, 24 + t²) and r2(s) = (6 – s, s – 4, s?) intersect? %3...

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Q: 5.Find the area of the surface generated by revolving the given curve about the y-axis. x= 19- y, - ...

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Q: Write a full solution  Let consider the following function: f (x) = 2(x + 1)^2  −8.  A) Find f(−2)...

A: Solution is written in step2.

Q: 1. y = 3x2 - 5x when x = 3 dx when x= 2 b. dt a. 32 dt dy dt

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: Find the volume obtained by rotating the region bounded by x = y² and ¤ = y around the r-axis. %3D

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Q: 12) y = esin t (In t5 + 10) A) eCos t (cos t)(In t + 10) - 5esin t 5esin t cos t B) C) esin t (cos t...

A: From the formula of derivative multiplication which is    d/dx[f1(x)*f2(x)] = f1(x)*d/dx[f2(x)]+f2(x...

Q: r each of the following shapes, set up a triple integral you would use to compute its mass, if its d...

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Q: Use the given functions to find each of the following and their respective domains. Do not try to si...

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Q: x² x² + x + 20

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Q: Let f(r) Find the values of x where f'(x) = 7. I + 8 Give exact answers (not decimal approximations)...

A: We will find the solution of given function as shown below

Q: Find the slope of the line shown below 4- -4 slope tim but

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Q: d. At what ordered pair location does the tangent line make contact with h(x)? (Give your answer in ...

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Q: 3. The disk and cylindrical shell methods for calculating the volume of a solid of revolution always...

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Q: Find the area of the surface obtained by rotatin the curve y = Va about the y - axis for 64 < x < 10...

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Q: af af and ax 'ay L: f(x.y) = (x + y)(2x + y)² Compute %3D дхду

A: Given that: f(x, y)=(x+y)(2x+y)2

Q: Use l'Hopital's Rule to evaluate the limit. cos 3x - 1 x2 21) lim x-0 A) - C) 0 D en len

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Q: x-3 Given the reciprocal function, x+5 A] Identify the vertical asymptote (x-int) and the horizontal...

A: The given problem is solved below in detail.

Q: If f(x) VI 2 find: VI + 2 f'(x)= f'(2) =

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Q: Find lim Itcos 2X メ 니(x- 폰) 2

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Q: Find all real solutions to 2x'3 -4x6 – 6=0. 1/3 1/6

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Q: 12. An arrow shot straight up from ground level with an initial velocity of 128 feet per second will...

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Q: In using the technique of integration by parts, you must carefully choose which expression is u. For...

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Q: 3x + 6 If f(x) find: 2x +2 f'(x) = f'(3) =

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Q: 1. Use the chain-rule and find x and ÿ in terms of x, i, and ä if: а) у3 4x? b) y= 10x3

A: To find y" in terms of x, x', x".

Q: Find the derivative of f (x) = arcsin (x²). 2x f' (x) = 1-a4 f' (x) V1-x4 2x O f' (x) = V1-a² O f' (...

A: Use differentiation of trigonometric function

Q: 1. Show that c(t) = (e¬t cos t, e-t sin t), 0 <t <∞ has finite length and calculate its valu

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Q: If P(a, b) is on the unit circle whose arc léngth from the point (1, 0) is t, which of the following...

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