1 X EXAMPLE 4 Investigate the following limit. lim sin x0

Q: Estimate the limit numerically or state that the limit doesn't exist lim x→0  sin(4x)/x

A: Before we get into the evaluation of this limit, let's recall the fundamental rule of limit as shown...

Q: Determine the values of A for which h(x) is continuous. (Enter your answers as a comma-separated lis...

A: h(x) is a polynomial function and will hence be otherwise continuous except at break points (where t...

Q: For what value of the constant c is the function f continuous on (-o, o)? { Cx2 2x if x < 5 - x3 f(x...

A: Observe that, f (x) has discontinuity at x = 5.If it is continuous at x = 5, then continuous on (-∞,...

Q: Calculus Question

A: Given velocity vector with initial position is

Q: Algebraically evaluate the following limit, if it exists. If it does not exist, explain why. If it d...

A: Given,

Q: The table below can be represented by a ______________________ ? x 0 1 2 3 y 21 ...

A: In this table, x values are increasing by 1. And y values are also increasing by 2.

Q: The volume of the solid obtained by rotating the region bounded by y=ex, y=lnx, x=1, and x=5 about t...

A: Consider the given curves.

Q: Evaluate the definite integrals

A: We substitute cosx =t and sinxdx=-dt

Q: Does there exist a real number c that makes the following functions continuous over (−∞,∞)? If so,fi...

A: If function is continuous at point of given interval, then

Q: Find all points of intersection (r,θ) of the curves r=4cos(θ),  r=1sin(θ). Next find the area inclos...

A: Given polar curves are r = 4 cos(θ), r = 1 sin(θ).Equate the r as follows.

Q: Graph C(q) = 3q + 2000 and R(q) = 8q on the same axes and find and label the break-even point, q0. (...

A: Graphed using graphing calculator.Red line is C(q) = 3q + 2000And Blue line is  R(q) = 8q they meet ...

Q: A company has a cost function C(q) = 3q + 2000 dollars and revenue function R(q) = 8q dollars Find t...

A: We know that , profit is the difference between revenue and cost

Q: Find the average value for 8 (b)

A: Definition:

Q: T=DC - 7, for D

A: To rewrite the given equation , with D as the subject

Q: Can I get help with this question step by step?

A: Sandwich Theorem : 

Q: If f(x) = x5 +x3+x, find f (f-1(2)).

A: Remember that a function is a relation in which every element of a domain has a unique image in codo...

Q: In a survey at a local university 52% of students say that they less than the recommended eight hour...

A: The problem concerns working out the percentages and interpreting .

Q: Can I get help with this question step by step?

A: The given equation is:

Q: (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve a...

A:

Q: Can you please help me step by step with this problem?

A: Given that the function

Q: Solve equation what would it be a solution no solution infinite solutions  X+ 3y = -1 3x + 9y =-9 My...

A: From x+3y=-1 we get x =-3y-1

Q: Identify all the types of transformations applied to y=f(x) to yield each of the given equations. Le...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Consider the following Table: Company’s Estimates of Cost and Revenue for a Product   q 500 ...

A: Given,

Q: Find the area of the parallelogram with vertices  A(−3, 5), B(−1, 8), C(3, 6), and D(1, 3).

A: We first have to find the AB and BC vectors. A(−3, 5), B(−1, 8), C(3, 6)AB=(-1 -(-3) , 8-5) =(2,3)BC...

Q: Can you please help me step by step with this problem?

A: The given function is f(x) = 2+x2.

Q: Can you help me step by step with this problem?

A: To find:

Q: Because of past use of leaded gasoline, the concentration of lead in soil can be associated with how...

A: (a) Obtain the log model for the given data as follows.Let the log model be L(x) = A + Bln(x). Consi...

Q: Differentiate the function y 2x log4(Vx) У' 3

A: Firstly, we use product rule of differentiation which states that (uv)'=u'v+uv'

Q: Just need Question 2b, p1-p4

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Find the complex zeros of the following polynomial function. Write f in factored form.   The complex...

A: Given: -

Q: Suppose that the total revenue realized by the Odyssey Travel Agency is R=f(x) thousand dollars if x...

A: 1. f(b)-f(a)/b-a measures rate of change of revenue from "a" thousand dollars to "b" thousand dollar...

Q: Can I get help with this question step by step?

A: The given limit is

Q: Find a scalar equation of the plane that contains the linex = 1 + t, y = 2 − t, z = 4 − 3tand is par...

A: Given,The plane that contains the line x = 1 + t, y = 2 − t, z = 4 − 3t.So, we can say that the plan...

Q: Determine the values of x for which f(x) is discontinuous. (Enter your answers as a comma-separated ...

A:

Q: Can you please help me step by step with this problem?

A: From the given graph, it can be clearly seen that the corresponding function is:

Q: Write the equation of the circle centered at (−3,5)(-3,5) with diameter 16.

A: Consider given point (-3,5) as the center of the circle and the given diameter is 16

Q: lim as x approaches 4 from the right of 8-2x/|x2-x-12| a. 2  b.-2  c. -1  d. 4  e. infinity

A: The given expression is,

Q: Can you please help me step by step with this problem?

A: To find the derivative of the given function (fractional power)

Q: 5. For f(x, y) 2x +y v 3i-4j find the rate of change of fat (1,2,6) in the direction of the vector =...

A: rate of change of the function at the given point along the given direction

Q: Draw a circle with an equation of x2+4x+y2−4y=1.

A: Given,

Q: Mr. Smith and Mr. Stein were driving to a business meeting 190 miles from their office. Mr. Smith dr...

A: Mr. Smith and Mr. Stein were driving to a business meeting 190 miles from their office.Since, Mr. Sm...

Q: There was a question on a previous assignment I had trouble completing. I was unable to fully solve ...

A: Consider the two paths y=x and y=x2 through the origin.

Q: what is calculus?

A: There are more than one explanation for calculus. I have produced some of them for you to understnd....

Q: The point P(16,8) lies on the curve y=√(x)+4 Let Q be the point (x,√x+4).A.) Find the slope of the s...

A: The points P= (16,8) and Q= (x, x^1/2+4) lies on the curve which is given by:

Q: 20. Which of the following vectors is normal to the surface In(x + y* -- z) = x-1 at the point where...

A: Given surface is

Q: In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 44 +...

A: To calculate the average temperature using integration

Q: How do I solve this?

A:

Q: Solve 83 and 85

A: Since you have submitted two questions, we'll answer the first question. For the second question ple...

Q: The median weekly earnings for 16-24-year-old men employed full time are given below. Median Weekly ...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Can you please help me step by step with this problem?

A: Using the differentiation formula. If u and v are two functions then,