If the profit function for a product is P(x) = 1800x + 75x^2 − x^3 − 74,000 dollars, selling how many items, x, will produce a maximum profit?

Q: Find dy dx and d²y dx² x = et, y = te-t

A:

Q: Find the exact length of the curve. x=e'−t, y=4e¹/2, 0≤t≤2

A:

Q: (b) Find parametric equations that represent the line segment from (-1, 7) to (1, 3) for 0 ≤t≤ 1.…

A:

Q: #2 Given the integral S√ S√ 4 cos(x²) dx dy 0 [FIN √4 y (a) Do not attempt to evaluate it yet.…

A: The value of integral is 2 and the detailed explanation is mentioned in attachmentExplanation:Step…

Q: With a present value of $130,000, what is the size of the withdrawals that can be made at the end of…

A:

Q: PLS ENSURE ITS RIGHT ANSWER DOUBLE CHECK TOO AND Solve this based on only contexts from Natural…

A: Values of x where tangent to y=x²(ln x)² is horizontal are,x=1x=e−1=e1​Explanation:We know that,…

Q: If a person takes a prescribed dose of 4 milligrams of Valium, the amount of Valium in that person's…

A: Given that a person takes a prescribed dose of  milligrams of Valium, the amount of Valium in that…

Q: Can you solve y = ln(2x-3)  in a simple fashion?

A: The solution is x = (ey + 3)/2.Explanation:We solve y = ln(2x - 3) for x  by eliminating the…

Q: 1. f(x) = (4 — x²)5

A: Second derivative test for local maxima and minima :

Q: Verify the identity.   cotangent x equals StartFraction sine 2 x Over 1 minus cosine 2 x…

A: The objective of this question is to verify the trigonometric identity cot x = sin(2x) / (1 -…

Q: Analyze the graph to the right to address the following about the polynomial function it represents.…

A: The given function

Q: 2 Determine the value(s) of x for which the tangent to y = x² (lnx)² is horizontal. Paragraph V BI…

A: The objective of this question is to find the value(s) of x for which the tangent to the curve y =…

Q: Reflect? Stretch/Shrink vertically? Stretch/Shrink horizontally? Shift up/down? Shift left/right? by…

A:

Q: Suppose you want to have $700,000 for retirement in 20 years. Your account earns 4% interest. a) How…

A:

Q: According to economic theory, the demand x for a quantity in a free market decreases as the price p…

A: Given:the number x of DVD players people are willing to buy per week from a retail chain at a price…

Q: 1. Find fr (1, 1) and fr (1, 1) where f(x, y) = 6√/2x4 + y³ − 2x+5xy.

A:

Q: (4/x3 + 1) dx

A:

Q: Need to Evaluate WITHOUT using a calculator! For: (Refer picture for the questions) (An…

A: 1) e-√2 2) -1 / ctn(46°)Explanation:1)  To evaluate the expression e(sin(-45)-sin(45)), let's first…

Q: Given 6 = 41 - 2j and d = -101 + 73, find 16+d| and |b|+|d|.

A: Given b→=4i→−2j→ and d→=−10i→+7j→.To find : |b→+d→|,|b→|+|d→|

Q: A new product has just come onto the market and is a big hit. The success, however, does not last…

A:

Q: 3. Find the value of the expression lim 2x2+5x-7 h-2 x-1

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: R is the region bounded above by the graph of f(x) = 2x and below by the x-axis over the interval…

A: Region is bounded by f(x)=2x23 and below by the x-axis over the interval[0,3].Rotating the region…

Q: Find the exact value of the expressions Bold cos left parenthesis alpha plus beta right…

A: The objective of this question is to find the exact values of the trigonometric expressions…

Q: 4. Use Equation 5 to find dy/dx. (a) y cos(x) = x² + y² (b) arctan(ry)=x+xy (c) e sin(x) = x+xy

A:

Q: Suppose that f is a function given as f(x) = x² + 2x + 3. Simplify the expression f(x + h). f(x + h)…

A:

Q: Evaluate the line integral foxy²²ds, where C is the line segment from (-1, -1, −1) to (1, 1, 1).

A: We have to calculate

Q: 72 3.(2.4) (1) Let c(t) = (sect, tant), — — < t < be a path. Find an xy-equation of this path. (2)…

A: Given that (1) Let  be a path. (2) Let  be a path.

Q: . Let G(x)= x+3)2, if x ≤ -1; 2-x if 1<<1; Find all values of a where G is not continuous. , if x 1.

A:

Q: Problem #3: Find the inverse Laplace transform of the following expression. 5s+6 2-6s+9

A:

Q: Let ā = (-1, -2, 2) and 6 = (0, 4, −4). Find the angle between the vector (in radians)

A: To find the angle between two vectors a→ and b, we can use the…

Q: Use integral tables to evaluate the integral. Sx√29x-7dx Click here to view page 1 of the Table of…

A:

Q: [4] Compute the area of the surface obtained by rotating the curve, x = 1 + 2y², 1 ≤ y ≤ 3, about…

A: given function

Q: Let f(x)=sin(x), find each of the following: find the second derivative, the thrid derivitie and the…

A: The objective of this question is to find the second, third, and fourth derivatives of the function…

Q: Given a = (-5,7) and u = (9, -4), find 3ã + 4ū. 3a + 4ū =

A:

Q: #9, Again, f(x,y) = x² + y² = xy-3x Find the absolute minimum and absolute maximum of fon the region…

A:

Q: Can you answer number 2,5,6,7 using integration by parts. Thank you.

A: Answer No. (2): To evaluate the following integral by using integration by parts.Note: Since you…

Q: Find the value of the expression lim t→ꝏ -e-3t +5 I want human solution please no AI

A: The objective of the question is to find the limit of the expression -e^-3t +5 as t approaches…

Q: if f(x)= 5 sin to the negative one power ( x to the thrid power) then what is f prime of x

A: The objective of the question is to find the derivative of the function f(x) = 5sin^(-1)(x^3). This…

Q: At what point on the given curve is the tangent line parallel to the line 3x - y = 6? y = 5 + 2e* -…

A: (x,y)=(ln(6),17−9ln(6))Explanation:

Q: Consider the indefinite integral 7x37x264x + 80 dx x²+16x2 Then the integrand has partial fractions…

A:

Q: 7. Determine if each of the following represents an exponential function. If it does, find the…

A: The general form of the exponential function is , where b&gt;0.

Q: Find two unit vectors orthogonal to both u = (4, −1, −3) and v = (0, 4, 1). Give exact values (no…

A:

Q: Sketch the level curve of the function z(x, y) = y² — x² for c = 16. - 10- 9 8 7 6 5 4 3 2 + -10 -9…

A: given function

Q: 5) The electrical Power given in Watts (W) produced in a certain battery is given by P= 144 r (r +…

A: Given that the electrical power given in Watts (W) produced in a certain battery is given by ,where…

Q: Find all local extrema for f(x)=x2e2x in the first cycle of the curve. Be sure to show a test for…

A: To find all local extrema for the following function. Note: Since, the student has mentoned to find…

Q: Let f(x) = x|x|. (a) Sketch the graph of the function. 2 y У 4 2 2 y 4 2 y X y X J -4 -2 -2 2 -4 -2…

A: a)4th graph is correct answer b) Differentiable for all real x  c) f′(x)=2xExplanation:

Q: (3) (LATEX question) Let n = N and take any cЄ R. Find lim x c xn- cn X - C

A: Let .To find the following limit.

Q: The population, P, of a bacteria colony at t hours can be modelled by: P(t) 450+130t+ 15t² + 2t3 a.…

A:

Q: Find the circulation of fluid motion F⃑(x, y) = xi⃑ − xyj⃑ along positively oriented ellipse x2 +…

A: The objective of the question is to find the circulation of the fluid motion along the given…

Q: Identify the inflection points and local maxima and minima of the graphed function. Identify the…

A: