Now, evaluate each of the following limits.

Q: Use the rules of differentiation to find the derivative of the function. f(t) = -5t² + 3t - 9

A: The function is f(t)=−5t2+3t−9The aim is to find the derivative of the function using the rules

Q: 9. The position of Minnie the mouse, as she moves back and forth along a horizontal line is given by…

A: Given that  position of Minnie the mouse given by equation is

Q: Calculate and type the final answer in the space. You may use either scientific notation or standard…

A: The given expression

Q: Textit) Find a formula for the parabola whose graph is given below: f(x) = (-2, 8) 4 (3, 8) (click…

A: To find the formula for parabola?Note- As per company guidelines for multiple questions posted we…

Q: Beginning with the graph of y = sin x, use shifting and scaling transformations to sketch the graph…

A: use the graphing tool to graph the function

Q: Find the tangent plane to the equation z = point (8, 16, 3). z = 2 3e²-48 at the

A:

Q: 77. Explain why or why not Determine whether the following state- ments are true and give an…

A: Determine whether the following statements are true and give an explanation or counterexample.Since…

Q: Find the domain of the following function. f(x) = √ 4 − 3x Explain how to solve this question in…

A:

Q: Consider the graph of a function f shown here: 3 (c) 6 ƒ(9) — ƒ(6) 9-6 (d) f'(3) ? 9 Using the…

A: From the given graph

Q: Evaluate the limit of the given indeterminate quotient. lim x→0 (√²+2-1). Number

A: given limit

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

A: The given function is

Q: Let s(t) = 8t³ — 24t² function for the velocity. 241² - 48-72 o(t) - 192t be the equation of motion…

A:

Q: The radius r of a sphere is increasing at a rate of 9 inches per minute. (a) Find the rate of change…

A:

Q: Consider the following two lines in space. t (₁ : x = 4+ 5+ y = 57st, z = 1-4t 6₂² x = 4 + t, y = −…

A:

Q: Find the differential dy of the given function. y = 7x²5 dy =

A:

Q: 39. A boatman wants to cross a canal that is 3 km wide and wants to land at a point 2 km upstream…

A:

Q: Find a quadratic function of the form y = ax² that passes through the point (-2,16).

A:

Q: Use long division to divide and use the result to factor the dividend completely (7x²9x - 10) = (x -…

A: Consider the following

Q: Two friends Korin and Lorie are running a marathon along a straight road. Assume that their…

A:

Q: 89. Explain why or why not Determine whether the following state- ments are true and give an…

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

Q: The area under the curve y = √x bounded below by the x-axis and on the right by x = 4 is 16/3 square…

A: Solution:Area=Let t=-x==Area==Area=Similarly,Area=Let t=xdt=dx==Area=

Q: or the function, find the points on the graph at which the tangent line is horizontal. y=x²-5 Select…

A:

Q: List the interval(s) on which f is increasing. The interval(s) on which f is increasing is/are (Type…

A:

Q: 30,000 Р Suppose that the demand function for a product is given by D(p)=- a) Find the demand as a…

A:

Q: Use the graph of f(x) below to find the following derivatives. Write DNE if the derivative does not…

A:

Q: Each derivative represents the first line of a "first principles" definition for some function f(x).…

A:

Q: 2 Consider the general quadratic function f(x) = ax² + bx + c, with a #0. a. Find the coordinates of…

A: Consider the general quadratic function f(x)=ax2+bx+c, with a≠0.

Q: Find the area of the shaded region. y = 0 2 square units y 2 -2 y=x√√4-x² y=0 2 X

A:

Q: Evaluate the definite integral. [₁²₁ (x^² + ²3 ) (x² + +7 + 2x)-² dx

A: Solution-

Q: In this problem, we walk through a general procedure of finding horizontal and vertical asymptotes…

A: The given function is

Q: Find the linear approximation to the equation f(x, y) = 4₁ xy 2 = 4√ at the point (2, 4, 8), and use…

A:

Q: Find the general solution of the differential equation. (4) 256y+) = 16y

A: Given that :-256y(4) = 16yWe find the general solutions of this given differential equation.

Q: f(x) = √√√x + 2; a = 7

A:

Q: Which of the following vectors is perpendicular to i? i+j i-j i - 2j -2i -2j None of the above

A:

Q: Analyze the function below. Which of the following is/are true? 8 f (d) 81 82 8 x+5 as x→ 1+, f (x)…

A:

Q: The graph of f(x) is given on the grid. Graph f'(x), its derivative. 8 7 96 5 4 3 2 1 -8-7 -6 -5 -4…

A:

Q: Let r(t) = (−5t5 + 1, −4e¯5t, sin(−2t)). 1 f F (1) Find [F(t r(t)dt (don't include the +C) r(t)dt =…

A:

Q: Evaluate the definite integral. Hint: Let u = x + 1. 8 [° 7x √x+1dx

A:

Q: Sketch the level curves of f(x, y) = y + 2x r² +3 at k = 0, 1 on a common Cartesian plane.

A:

Q: Evaluate the limit sin 3x 8x lim x→0

A: given limit

Q: Solve the given differential equation for x € (-∞, -1) U (1, +∞) 1- y² 1 x² y' =

A: The given differential equation is

Q: Find the integral using an appropriate trigonometric substitution. 1 x²√√x²+25 dx

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Suppose that f(x) = 1+5x. Consider the partition P of the interval [-2, 1] by means of the set of…

A: Given that :Equation of the function Interval is Set of partitions are To find : Reimann sumConcept…

Q: 1 Find the inverse function (on the given interval, if specified) and graph both f and f on the same…

A: The given function  for .The aim is to find the inverse function and sketch its graph.

Q: Evaluate the following limits at infinity. 2³-42² 2x³+1 a) lim 100 b) lim 8118 3-41² 2z³+1

A: We need to evaluate the following limits:We can evaluate this as follows:

Q: (Text Suppose y = f(x) graphed in the figure below represents the cost of manufacturing x kilograms…

A:

Q: 3. Consider the curve y = x² for 0 < x < 3. Set up, but do not evaluate, the integral expressing:…

A:

Q: 1. Evaluate lim 818 x5 +999x4 + 453x² 3x5 + 13 Indicate the limit laws you use.

A: We have to find the limit value of the given question no.1.We divide numerator and denominator by…

Q: Use the Squeeze Theorem to evaluate the limit Enter DNE if the limit does not exist. Limit = lim sin…

A:

Q: Determine, with justification, whether the following series converges: 1 10. Ln=11+√n 80

A: