Use calculus to derive the volume of the unit sphere.

Q: Consider the space curve "(t) = (−5t + 4, −5t - 3,5t + 4). a. Find the arc length function for r(t).…

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Q: 1. Calculate the difference quotient, simplify your final answer. f(x+h)-f(x) h for the function f…

A: Answer is in step 2.

Q: Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line…

A: Given that a line passes through point  and parallel to line

Q: Example 8 Video Example) Find f'(x) for f(x) = sin(cos(tan(x))). Solution d f'(x) = cos(cos(tan(x)))…

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Q: Suppose the derivative of a function fis f'(x) = (x + 2)²(x-4)³(x − 6). On what interval is…

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Q: Let f(x)= = - [₁ f'(x) = f'(2) = todt. Evaluate the following.

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Q: Find all vectors  v = that solve the given vector equation:  v ✕ i = 4j   A) v =   B) v = with a ∈…

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Q: If f and g are the functions whose graphs are shown, let u(x) = f(g(x)), v(x) = g(f(x)), and w(x) =…

A: Given that:-

Q: f  f(x) + x2[f(x)]4 = 18 and f(1) = 2,  find  f '(1).

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Q: Consider the function R(t) as representing the value of an ounce of palladium in U.S. dollars as a…

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Q: 68-72. Higher-order derivatives Find f'(x), f"(x), and f""(x) for the following functions. 68. f(x)…

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Q: Find all numbers b such that the average value of f(x) = 3 + 10x - 6x2 on the interval [0, b] is…

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Q: Problems 20-23, Determine whether each function is even, odd, or neither. 20. f(x) = x² - 2x4 21.…

A: Given,

Q: Differentiate the function. 6w² P'(W) = P(w) = 4w + 8 VW

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Q: lim 2 76. Sketch a graph of a function with the following properties: f(x) = 1. f(x) = 3. f(x) = 6,…

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Q: Problem 2 H 4). The Newton's Law of Cooling says that the rate at which a body cools is proportional…

A: By Newton's Cooling Law = Proportionality constant Temperature of the surrounding Temperature of the…

Q: If a ball is thrown in the air with a velocity 50 ft/s, its height in feet t seconds later is given…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 2 cos(t) +…

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Q: 2. Use the given values of " to set up a table to evaluate the limit. Round your solutions eight…

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Q: 2 x-3 Find the slope of the secant line on the graph of f(x) for each interval: Let f(x) =

A: given function

Q: Consider the following. |x + 41 lim X-4 X + 4 -10 y 4 2 -2 5 10 X Use the graph to find the limit…

A: Given that a limit problem and we solve this problem by using general property of limit.

Q: y = x³, y = 0, X = 1, X = 4

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Q: M = units (Simplify your answer.)

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Q: need help

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Q: Match the description of the activity in the answer bank to the day component where it occurs.

A: Here's how the activities match the day components:

Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: The given figure

Q: In 2017, the world's population reached 7.41 billion² and was increasing at a rate of 1.1% per year.…

A: (a) To write a formula for the world population (in billions) as a function of the number of years…

Q: 6. Degree 4; zeros: 2 + i;

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Q: Show that the curve of y = 9e^ + 5x + 4x" has no tangent line with slope 4. First, calculate the…

A: Given function As we know that slope of the function

Q: √(-1-x); (4) Let g(x) = { x²; 3x - 5; if x < -1 if -1 < x < 2 if x ≥ 2. (b) Sketch the graph of y =…

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Q: Question What value(s) of 8 are an appropriate choice when proving the following limit? lim (√√8x32)…

A: We have to find the delta using the epsilon-delta definition of a limit.

Q: (4) A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells z…

A: A soft-drink vendor at a popular beach analyzes his sales records, and finds that if sells x cans of…

Q: TT/3 π/4 dx cos² x tan x

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Q: Problems 10-12, Use the given zero to find the remaining zeros of each function. 10. f(x) = x³2x²…

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Q: Solve the initial-value problem d²y dt² dy dt +14- +49y0, y(1) = 0, dy (1) = 1.

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Q: (2) The population of the world in 1995 was about 5.7 billion, and the estimated relative growth…

A: Standard equation of exponential growth is Y = a ( 1 + r) x WhereY = Population after x yeara =…

Q: lim h→0 lim h→0 lim h→0 lim h→0 −(2+h)² +3h+4 2 -(2+h)² + 10 2 -(2+h)² +3h+4 h -(2+ h)² + 10 h

A: We are to evaluate the given limits.

Q: u = cos 0 i + sin 0 j cuando (a) 0 = 00 y

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Q: Find the volume of the solid that results when the region bounded by the curves y = 2x², y = x, and…

A: To find the volume of the solid that results when the region bounded by the  curves , and y-axis is…

Q: Find the absolute maximum and absolute minimum values off on the given interval. F(x)=In(x2 + 3x +…

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Q: Find the average value fave of the function f on the given interval. x² (+3 (x³ + 9)² f(x): = [-1,…

A: Find the average value fave  of the function f on the given interval.f(x)=x2(x3+9)2,[−1,1]

Q: Find the gradient of the function at the given point. f(x, y) = 3x + 4y² + 2, (3, 1) Vf(3, 1) = = X

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Q: (5) Given f(x) = 3*, g(x) = log3 x, h(x) = 2-log3 (x - 1), sketch their graphs on the same ry-plar…

A: The given functions are

Q: For the situation described, write the right-hand-side of a differential equation that is a…

A: It is given that the rate of change of the velocity with time is proportional to the difference of…

Q: Test the series below for convergence using the root test. 2n 10n + 4 The limit of the root test…

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Q: Use the Squeeze Theorem to show that lim (x² cos 22x) = 0. Illustrate by graphing the functions f(x)…

A: given limit

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Question What value(s) of d are an appropriate choice when proving the following limit? lim (8x1) =…

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Q: 1) On which derivative rule is the method of integration by parts based? (product rule, quotient…

A: Given the different formulation forintegration-by parts.

Q: Use h(x) = CX + 1 11x + C to answer the questions below. (a) Find the value of c so that h(x) has a…

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