3. A particle moves according to a law of motion s = where t is measured in seconds and s is measured in feet. (a) Find the velocity at any given time t. (b) (c) What is the velocity after 3 seconds? = t¹ – 2t² + 1, t > 0, When is the particle at rest?

Q: atives of point (x, y) = (2, 3).

A:

Q: 9. Assume that the oil spilled from a ruptured tanker spreads in a circular pattern (A = πr²) whose…

A:

Q: #6: For which of the following can we use intermediate value theorem with the interval [a, b] = [0,…

A:

Q: Given F(r, s, t) = -r (3s5 + 6t5), compute: Frst

A:

Q: A 5-th degree Taylor polynomial of a function f(x) at × = 0 could potentially have the form (select…

A: A polynomials are given.The aim is to find the  degree Taylor polynomial of a function  at .

Q: Find the derivative of the function. h'(t) = h(t) = 17 cot ¹(t) + 17 cot-1 ¹(+) X

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

Q: If x² + y² + z² = 9, dz dt dx dt X dy = 4, and dt dz = 6, find dt when (x, y, z)= (2, 2, 1).

A:

Q: Consider the functions f(x) = √√ and g(x) = x + 4. a. Find and simplify (fog)(x). Determine its…

A: Given, .

Q: The definite integral: Use geometry to find (2+√9-x²)dx. a.

A:

Q: Solve the following exponential equation. Use logarithms to express the solution in its exact form.…

A:

Q: Evaluate the following limit. (7x² - y²) lim (x,y)→(6, -6)

A: Let,

Q: 2. Find the angle of intersection between the curves y=x² +5x-8 and y=x²-2x+6 to three significant…

A:

Q: Find the directions in which the directional derivative of f(x, y) = x² + xy³ at the point (3, 1)…

A:

Q: = (a) Draw the exponential function: y 3x Also identify the asymptote to this function in your…

A:

Q: Consider the functions f (x) = √√ and g(x) = x - 10. a. Find (f + g) (x) and determine its domain.…

A: Given,

Q: Verify that fxy = fyx for the following function. f(x, y) = 3x5y6-9x4y³ fx =

A:

Q: The length that a hanging spring stretches varies directly as the weight placed at the end of the…

A: The length that a hanging spring stretches varies directly as the weight placedat the end of the…

Q: < Consider the surface z = f(x,y)=√1-x² - 2y² and the oriented curve C in the xy-plane given ¹,…

A:

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

A: Given, .we know, .

Q: Winter Fun will supply a Blazing Blue snowmobiles at price p in dollars for each Blazing Blue…

A: Given

Q: 1. Suppose that a population develops according to the logistic equation = 0.5P 0.0025P2 where t dt…

A:

Q: Write an equivalent integral with the given order of integration a = b 2 2-1 x [² ²² ² F(x, y, z)…

A:

Q: Differentiate the following function. Simplify the derivative. G'(x)= G(z) =√10 – 8e¹z

A:

Q: Inverse Laplace transforms can be found using the linearity property of transforms and a reference…

A: The linearity property of Inverse Laplace Transform:Where  and  is the constant.And the Inverse…

Q: Evaluate the integral using partial fraction method. Sex ((x^² + 7) dx (x²+2)(x-3)

A: To evaluate the following integral by sing partial fraction method.

Q: 4. Give the phase shift, vertical displacement, amplitude, and period of the following function: ==…

A: To give the phase shift, vertical displacement, amplitude, and period of the following function.

Q: a. x 2 b. C. lim f(x) d. lim f(x): x+2+ = lim f(x): x 2 Consider the graph of the function y = f (x)…

A: If the function has a left hand limit and right hand limit at a point and both are equal. Then, the…

Q: Let g(x)=9x² - 9. (a) Find the average rate of change from 5 to 6. (b) Find an equation of the…

A: we need to find out the average rate of change and also the equation of the secant line.

Q: 3. Write the equation of the tangent to x² + y² + 2xy = 4 at the point (1,1).

A: x ^ 2 + y ^ 2 + 2xy = 4

Q: 1. 5x+7 ܐ ] x3+ 2x – x =2 dx

A:

Q: Find an equation of the tangent line to the curve at the given point. y = xe−x2,    (0, 0)

A: Given, ,  point is (0,0).

Q: (FRQ No Technology) The graph below represent f'(x), the derivative of f(x) on the interval [-4,6]…

A: Given graph of f'(x)

Q: Sunset Lake is stocked with 2600 rainbow trout and after 1 year the population has grown to 7000.…

A:

Q: 1. Suppose that a population develops according to the logistic equation is measured in weeks. a)…

A:

Q: let f(x) = logb(9x^7-8). For what value of b is f′(1) = 9?

A:

Q: The solution was solved for washer instead of disk

A: We have to find the volume using disk method.

Q: Evaluate the integral using Pattial Fraction method (x²+7) dx (x²+2)(x-2) S&

A: We will solve the given  integral using  partial fraction.

Q: A particle moves with position function s = t44t²³36t² + 15t, t≥ 0 (a) At what time does the…

A: Velocity function of a particle  is the first derivative of the position function of that…

Q: ind the difference quotient of​ f; that​ is, find f(x+h)−f(x)h​, h≠​0, for the following function.…

A: The given function is As we know The difference quotient is

Q: Which of the points P = (-1,4,-7) and Q = (6,-1,5) is closest to the z-axis? OQ (6,-1,5) OQ (6,-1,0)…

A:

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: We have to find the absolute maximum and minimum values of the function over the indicated interval,…

Q: Use the Chain Rule to find dz dt 1 where z = 3x siny, x = t², and y = 2t4.

A:

Q: Let f be a continuous function and set Evaluate the following (a) F'(x) (b) F'(1) (c) F"(x) (d)…

A: Let  be a continuous function and set To evaluate the following.

Q: Using a telescope, you track a rocket that was launched 6 km away recording the angle between the…

A:

Q: The graph of f(x)=x is shifted left 5 units to arrive at the graph of g(x). What is the rule for…

A:

Q: An arrow is shot into the air and moves along the parabolic path y=x(50-x) (see figure). The…

A:

Q: 3. Graph the Exponential Distribution equation f(x): = .8e-8x

A: We have to graph the exponential distribution equation…

Q: A tank contains 1140 L of pure water. Solution that contains 0.03 kg of sugar per liter enters the…

A: The tank has 1140 L of pure water.Solution has 0.03 kg of sugar per liter enters the tank at 3 L/min

Q: Find the an equation of the hyperbola satisfying the given conditions. Foci at (-13,0) and (13,0);…

A:

Q: (i) (k) dx (tan x) dx (secx) = = (j) (cscx) = dx (1) :(cotx) = =

A: As per your request, we answer only parts (j) , (k) and (l).find using derivative rules