Determine the velocity of progress with the given equation: D = 20t + 5/t+1 when t = 4 seconds.

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Q: Evaluate the following limit. lim x³e -x² xxx = Note: Input DNE, infinity, and -infinity for does…

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Q: 16. x1 + 3x2 +4x3 = 0 3x1 + 8x2 + 7x3 = 0

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

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Q: 2. Use Calculus to find all local extrema of the function g(x)=x√3-x.

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Q: Compute the following limit using L'Hospital's rule if appropriate. lim (√2³-42² - 2) = I->∞0

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Q: In 2011 a country's federal receipts (money taken in) totaled $2.46 trillion. In 2013, total federal…

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Q: inld4u trated 1. T1: I can apply mathematical definitions. 8\II out frowemdit coin 11 auber a ora ea…

A: Limx-infinity (lnx+x)/(x+3)

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Q: Find the maximum and minimum values of the function f(x, y) = 2x² + 3y² - 4x - 5 on the domain x2 +…

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Q: = O Trigonometric Identities and Equations Proving an identity using fundamental trigonometric…

A: 1+tan2x

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A: To determine the inverse Laplace transform.

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A: we are given the cost function and we need to find out the marginal cost function.

Q: Evaluate the definite integral by interpreting it in terms of areas. 7 (3x - 18)dx 3

A: To evaluate the following definite integral by interpreting  in terms of areas.

Q: Consider the curve r(t): = og(t)i + e-tj+ + 5k for t > 2. Calculate limt →+∞ r(t) (if it exists). е

A: Find the limit

Q: J 4³ (u + 1)² du

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Q: a 5. At 2:00 PM jogging at 8.5 mph. starts from the same place, heading East at 60 mph. the driver…

A: At 2:00 PM a runner heads east on a highway, jogging at 8.5 mph. At 3:00 PM, a driver starts from…

Q: Find a formula for the nth term of the sequence where an is calculated directly from the value of n.…

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Q: Suppose T: R² R³ is a linear transformation. Let u, v and w be the vectors given below, and suppose…

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Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the…

A: The given graph

Q: Suppose that 3 J of work is needed to stretch a spring from its natural length of 34 cm to a length…

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Q: C T 3 2 1 To find the blue shaded area above, we would calculate: b So f(x) dx Where: 1 2 3 4 f(x) =…

A: We have to use the graph to find the integral substitutes and area  under the graph

Q: Let f(x, y) = x sin(x + y) (a) Calculate the directional derivative of f at the point (1,-1) in the…

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Q: 2. a. C. Determine the critical number(s) for the following functions. f(x) = 17-6x + 12x²…

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Q: Find f. f(t) f'(t) = t³ + -/-/7₁ t5 t> 0, f(1) = 4

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Q: 6. Let f(x, y) = sin(x + y). Answer the following questions. (a) ) Find the gradient f(x, y). (b)…

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Q: 8. Consider the gradph of the function f(x, y) = x² - 5xy given by z = x² - 5xy (a) ( (1,2). Find an…

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Q: Consider the following. {-x³ +3, -x² + 4x, x≤0 x > 0 Find the critical numbers. (Hint: Check for…

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Q: f(x)=x²8x² + 5

A: f(x)=x4−8x2+5

Q: d Find ax(-3x-4).

A: We need to find the following derivativeFormula Used:

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Q: Evaluate the integral by converting to polar coordinates. 3 S³ S 0 9-x² cos(x² + y²) dy dx = 0

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Q: 0 -3 5 1 0 1 0 6-58 0 -1 -1 3 4 -2 0

A: The given determinant is

Q: 2. Exponential Growth: The table below represents an exponential function. Find the missing values.…

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Q: Evaluate the following integral 6x + SS (8x - y) In (8x - y) dA R where R is the region bounded by…

A: Given that, where R is the region bounded by the graphs of                  Using the change of…

Q: (a) Find the unit tangent vector on the curve r(t) = [cos(t), -t, -4sin(3t)] when t = 0.

A: Since you have asked multiple questions in a single request so we will be answering only first…

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Q: Sketch the region enclosed by y = 7x and y = 8x². Decide whether to integrate with respect to x or…

A: In this question, we will find the area of the region.

Q: For y = f(x) = 7x², find f(x₁+AX)-f(x₁) Ax || f(x₁ +Ax) -f(x₁) Ax given x₁ = 5 and Ax=2.

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Q: If y xy + x² + 1, then when x = 01/1/12 0 - 12/1/20 O nonexistent O -1 O-2 -1 dy d = ? dx

A: we need to find out the derivative of the function at the given value of x.

Q: Consider the curve r(t) = (t² + 1)i + tj + (2t² + 3t)k. What is the velocity? What is the accelera…

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Q: 1 3 2 1 a To find the blue shaded area above, we would calculate: ·b [ f(x) dx = area Where: f(x) =…

A: The given graph

Q: Consider the function f(x) = 2x³ + 3x² - 36x - 54. a. Find the first derivative. f'(x) = b. List any…

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Q: Solve 2(cos2x)y' + ysin(2x) = 4cos4x 0 =< x < pi/2

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Q: Knowing that sin(0.65) is about 0.6, find cos(0.65). What relationship between sin(0.65) and…

A: sin(0.65) = 0.6

Q: PROBLEM No. 2. Solve the following differential equation by the method of undetermined coefficients:…

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Q: The graph of y = f(x) is given below. -5 150 num -4 lim f(x) AI-1 -3 -2 5 4 3 2 -1 -1/ 1 2 4…

A: A graph of the function  is given.The aim is to find the given limits.

Q: 3) Prove the following statement using the Intermediate Value Theorem (IVT): 2+3* = 4* has a…

A: Question No. (3):To prove the following statement using the Intermediate Value Theorem (IVT):  has a…