The quarterly profit (in thousands of dollars) of Cunningham Realty is given by P(x) x2 + 5x + 34 (0 < x< 50) where x (in thousands of dollars) is the amount of money Cunningham spends on advertising per quarter. (a) Find P'(x). 2. P'(x) = -x + 5 (b) What is the rate of change of Cunningham's quarterly profit if the amount it spends on advertising is $11,000/quarter (x = 11)? (Round your answer to three decimal places.) $ 600 X per dollar spent on advertising What is the rate of change if it spends $35,000/quarter (x = 35)? (Round your answer to three decimal places.) $ -9000 per dollar spent on advertising

Q: Solve the equation  by variation of parameters. y′′ + y′ =x.

A:

Q: evaluate using the Squeeze Theorem.

A: cos lies between -1 to 1 Then multiply both sides by (t2-4) and apply the limit   

Q: 2. Give counterexamples to show that these statements are false: (a) If f(c) is indeterminate, then ...

A: 2a) This function is indeterminate at x=0  So, we have shown that although f(0) is indeterminate, ...

Q: evaluate using substitution.

A: We substitute x=3

Q: Let P(x) = x³ –- 2x² + 10x – 1.83 i) Evaluate P at x = 1.96 (use 4 digit rounding arithmetic). ii) F...

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 general solution. 1. y′′ + 4y′ + 6y = 0 2. 6y′′ - 5y′ - 6y = 0 3. 4y′′ + 16y′ + 52y = 0

A: Since you have asked multiple questions in a single request, we will be answering only the 1st quest...

Q: Find the equation of the circle shown in the figure.

A: To determine the equation of circle.

Q: 3. Find the area of the region that lies inside the circle r - 1 and outside the cardioid r = 1 – co...

A:

Q: Which of the following is a verbal version of the Product Law (assuming the limits exist)? (a) The p...

A: By the product law we know that  This means the limit of the product is the product of the limits. ...

Q: sketch the graph of f . At each point of discontinuity, state whether f is left- or right-continuous

A: We first make table for both pieces x -1 0 1 y 1 0 1 Because of this part, there is a close...

Q: Give an example of a vector field F (x, y, z) that has value 0 on a surface and such that curl F is ...

A:

Q: Vx- 1 lim х—1 х — 1

A: We rationalize the numerator   

Q: Sketch the surface r = 2y? + 32².

A:

Q: B. Solve the following system of equations using Gaussian elimination. x - 2y = 2 – 3z; 3x + 4z = 4 ...

A:  

Q: Find the value of a that makes the following function differentiable for all values of x. ax if x<0 ...

A:

Q: Marginal Revenue Functions  The management of National Electric has determined that the daily margin...

A: Find the revenue function R(x) using the indefinite integration.

Q: y? – y – 2 y2 + y -6' lim f(y), where f(y) = f(y) 1.998 f(y) 2.002 2.001 1.999 2.0001 1.9999

A: We first simplify the function for y not equal to 2  

Q: determine the points of discontinuity. State the type of discontinuity (removable, jump, infinite, o...

A: tan(sinx) is a fully continuous function

Q: Let p and q be integers with q > 0. If y = x, differentiate the equivalent equation y = x° implicitl...

A:

Q: Let α(x) = ex2 . Verify the identity (α(x)y)' = α(x)(y' + 2xy) and explain how it is used to find th...

A:

Q: Suppose u and v are functions of x that are differentiable at x = 0 and that u(0) = - 4, u'(0) = 7, ...

A: i) We use the product rule  

Q: -3 Given matrices A-B and B- and B= , verify that det (AB)= det(A). det(B). Find the third Taylor's ...

A: (i) 

Q: 23. GU An advertising campaign boosted sales of Crunchy Crust frozen pizza to a peak level of So dol...

A:

Q: 5.5 12

A:

Q: Suppose that f (x) &lt; 0 if x is positive and f (x) &gt; 1 if x is negative. Can f be continuous at...

A: f(x) will be continuous at x = 0 if LHL = f(0) = RHL

Q: Suppose that f and g are discontinuous at x = c. Does it follow that f + g is discontinuous at x = c...

A: Let us define that Then both f and g are discontinuous at x=2   

Q: 3. O Find the intervals on which f is increasing or decreasing. 2Find the local maximum and minimum ...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: (a). Find the derivative of the given function. Simplify and express the answer using positive expon...

A: Since you have asked multiple questions in a single request, we will be answering only the 1st quest...

Q: Is lim x→10 20 equal to 10 or 20?

A: 20 does not depend on the value of x. So for all values of x , 20 will stay 20.  Even when x approac...

Q: 5.4.   11

A: Given function and interval  

Q: Set up the integral for the common interior of r1 and r2. r1 = 3 + 3 cos theta  r2 = 3 sin theta

A:

Q: Let  f(x) = −3x2 + 2,  and compute the Riemann sum of f over the interval  [1, 2]  by partitioning t...

A:

Q: Show that lim 1+ = e* for any x> 0. Let c= Rewrite the limit in terms of c. Choose the correct answe...

A: Given,  

Q: Can instantaneous velocity be defined as a ratio? If not, how is instantaneous velocity computed?

A:

Q: The integral ∫0π tetdt depends on t   True or False?

A: Given,

Q: dt to

A:

Q: 1) y = - x3 + 8x2 – 5x + 3 a) Graph "y". Be sure to label all maximum and minimum points and interce...

A:

Q: Use the Quotient Law to prove that if lim f(x) exists and is nonzero, then lim x→c f(x) lim f(x)

A: By the quotient law of limit, we know that   

Q: Show that there are infinitely many solutions to the boundary value problem y′′ + 4y = 0, y(0) = 0, ...

A:

Q: A stone is tossed vertically into the air from ground level with an initial velocity of 15 m/s. Its ...

A: We use the average velocity formula  

Q: Solve the equations in Exercises 1–5 by the method of undetermined coefficients. 1. y′′ - y′ - 2y = ...

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST QUEST...

Q: Find the derivative of the function. F(x) = et dt F'(x) = %3D

A: We know that by Leibniz rule of differentiation under integral sign, we have

Q: 8. Solve the triangle with B = 105°, a = 13 and c 18. Round the measures of the unknown side and ang...

A: We sketch the triangle roughly   

Q: evaluate using substitution.

A:

Q: Find the on y^2=8x whose focal distance is 10? please explain step by step along with cases.

A:

Q: evaluate using the Squeeze Theorem.

A: We know that sin is always  between -1 to 1 Multiply all sides by (x-1) and then take limit x-&gt; ...

Q: In a drama class, 5 students are to be selected from 24 to perform asynchronized dance. In how many ...

A:

Q: What is the power series representation of (cos(x^2))/x^2?

A: Let the given function Use the expansion of function cos x as  

Q: 5.3   1. b.   can you help with B

A: (b) Use the properties for the definite integral to find A (x).

Q: メp 25+(5-x)

A: