Find the average rate of change of the function over the given interval. f(t) = = 4t² - 1, [3, 3.1] Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval. left endpoint right endpoint

Q: Determine the value(s) of x for which f(x) = − 9x² +7x+2 has a horizontal tangent line. If there is…

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Q: 3. Check your understanding - Compute the following derivatives using the basic differentiation…

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Q: The graphs of the function and its derivative are shown above for -1≤x≤4 . (a)      Find the…

A: As per our guidelines we can answer only 3 sub parts of the given question so kindly repost the…

Q: Q4. Let x denote the grams of gold obtained in a ton of ore. Consider the two events A = {0 < x < 3}…

A: As per our guidelines we are allowed to answer only three subparts of the given problem. Kindly…

Q: Set up an integral which represents the arc length of y = O√1+36x¹0 dx OS √1+ 6x¹0 dx √1+36x¹2 dx O…

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Q: In this exercise, we will compute the definite integral 13z (z — 4)| dz. Yes, that's an absolute…

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Q: calculate all four second partial derivatives for the function f(x,y)=xe^-3y +sin (2x-5y)

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Q: 2. Given the graph of the function f shown below, determine which of the following statements is…

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Q: Find k such that the line is tangent to the graph of the function. Line Function f(x) = k√x y = 3x +…

A: To find  such that the line is tangent to the graph of the function.Finction: Line:

Q: 3. 1 2 4 -3 Let A = and let f(x) 2x3 4x + 5, g(x) g(A). Remark. In the evaluation of f(A),…

A: A=[1   2     4    -3]f(x)=2x3-4x+5g(x)=x2+2x+1Findf(A) and g(A)

Q: Find all points on the circle x² + y² = 100 where the slope is ) (smaller y-value) (x, y) = ( (x,x)…

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Q: How far away he is from the lamp post (60 ft) is irrelevant?? I have looked at other websites also,…

A: Distance of man from Lamp post  is irrelevant for the given question.

Q: V-3 7. lim 9-3 3 (²7³) - <=0

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Q: Given u = [50] and v = [3 4], a) Graph these two vectors u and v b) Determine whether the angle…

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Q: For f(x)=x² and g(x)=x²+2, (a) fog (b) gof find the following composite functions and state the…

A: The given functions are  and .The aim is to find the composite functions  and .

Q: In Problems 11-14, solve the given initial-value problem. =y³x³, y(1)=2 11. xy2) dx

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Q: form the follo x² + y²-2x-6y= 2

A: Given equation is as follows

Q: Identify a function f that has the given characteristics. Then sketch the function. f(2)= 8 f'(x) =…

A: Since the function f(x) has a constant slope of f'(x) = 3 everywhere, so f(x) must be a linear…

Q: f(x) = 3+x 5 Find each of the following. Be careful - you only have 3 tries! a) f(-2) = b) f(1) = c)…

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Q: The trigonometric substitution x - 2 = 3 sec could be useful in integrating a function (i.e., an…

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Q: eliminate arbitrary constants. Show complete solution. y= Ax + Bx²

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Q: Find the values of a and b that make f continuous everywhere. 1 -- f(x) = x² - 4 X-2 ax² - bx + 3…

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Q: 14. Are the functions continuous on the given interval? 7 (a) f(x) = 3 x € [1,7] and (b) g(x)=2x²-₁,…

A: For a function to be continuous on a given domain D, the function need to have finite values for…

Q: 19. dy dx = yex, y(0) = 2e

A: As per the guidelines I am supposed to solve one question at a time. Please repost the other…

Q: Question 11 Find the average rate of change of g (x) = -1x³ + 1 from x = -1 to x = 4 - Question…

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Q: Use the Quotient Rule to find the derivative of the function. cos(t) t6 f(t) = =

A: The given function is .The aim is to find the derivative of the given function.Quotient rule: Let…

Q: Use mathematical induction to prove that if the set S has N elements, then P(S) has 2N elements.…

A: Principal of Mathematical Induction Step (1) Prove the result is true for n=1Step (2) Assume that…

Q: Use the function f and the given real number a to find (f ¹)'(a). (Hint: See Example 1. If an answer…

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Q: 26. dy dx 2xy² + 3x²y², y(1) = −1

A: We have given,   dy/dx = 2xy2 + 3x2y2    y(1) = -1

Q: How many types of differential equations are there ? And what does each one look like ? For eg the…

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Q: 15. Which of the following is a perfect number: a) 496 b) 632 c) 694 d) 362

A: Question no. (15): To determine the perfect number.Note: Since the student has posted multiple…

Q: Let f(x)= x2, and compute the Riemann sum of f over the interval [4, 6], choosing the representative…

A: We need to find the Riemann sum of f(x) = x^2, over the interval [4,6].The formula for the Riemann…

Q: 2. lim u 2 4u+1-3 u-2

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Q: 2. Consider the function, f(x) = 2x + 2. a) Givene> 0, find 8> 0 so that if 8 0 f(x) -도<2x+ㄹㅅㅌ ㄹㄹ ㄹ…

A: In this question, we will find the limit by using the episilon-delta definition.

Q: Which of the following functions are continuous on the interval 1 < x < 7? A. h(x) B. f(x) = 2² +²36…

A: In this question, we will check the given function is continuous.

Q: Trace or copy the graph of the given function f. Assume that the axes have equal scales. Use…

A: given

Q: lim 8118 12x² - 15x - 12 x³ − 3x + 1

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Q: Use logarithmic differentiation to find dy/dx. dy dx || y = 2 9 V x2 + 9 x>3

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Q: In great detail, evaluate the following sequences for convergence or divergence: (a) { (b) {sin (n)}…

A: The given sequences are The aim is to find the given sequence convergence or divergence.

Q: 2. Find parametric equations for the line through the point (7,7, 1) with a direction vector d = A

A: Point (7,7,1)d=[1      6      2]

Q: For the position function s(t)= - 16t² + 102t, complete the table shown below with the appropriate…

A: The position function is given asWe know that , The average velocity formula over the interval [a,b]…

Q: Determine the critical point of the function and use the critical studied to classify it(s) as a…

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Q: 5. Consider the region R bounded by x = 12(y²y³) in the first quadrant. Use the method of…

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Q: Let h be the function given below. On which of the following intervals is h continuous? You may not…

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Q: Find an equation of the sphere with center (-1, 1, -2) and radius 4. = 0 Note that you must move…

A: We are given the center (-1, 1, -2) and radius(r)=4 of the sphere and we need to find out the…

Q: Find the derivative of the function. y = 7(6 - x²)6 Step 1 Apply the general power rule which states…

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Q: Find the Laplace Transform of the function f(t) = te¯t by evaluating the integral -t F(s) foto e 0…

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Q: Evaluate each expression using the graphs of y=f(x) and y = g(x) shown below. a) (gof)(8) b)…

A: given graph of the f(x) and g(x) to evaluate the expression

Q: Question 17 Use the limit definition of the derivative to find the slope of the tangent line to the…

A: By using the definition of the limit of the derivative to find the slope of the tangent line to the…

Q: Find the slope of the tangent line to the graph of the function at the given point. y = ln x4 y 6 K…

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