Problem 2 Consider the function f(x) = e* (sin x - 1) where x = [0,2]. Answer and show work for all of the following questions: (a) Find f'(x), show work and simplify your answer. (b) Find f"(x), by first simplifying f'(x) and going from there. Show work and sim- plify your answer.

Q: Calculate the integral of ƒ(x, y, z) = e² over the tetrahedron W in the figure (the region in the…

A:

Q: Find the derivative of s(t) = 1+sint 1+cost

A: Given query is to find the derivative of the expression.

Q: Find the critical numbers for f(x) = tan(x) - 4x TT on the interval [0,

A:

Q: Find d²y dx² if x=5+ t², y=t-t³

A:

Q: Solve the differential equation. 5 y

A:

Q: Find the area inside r = 3 + 3 cos θ and outside r = 3 + 3 sin θ in the first quadrant

A:

Q: 1 Find an equation for the line tangent to the graph of y = tan 1 What is the tangent line to…

A: Topic - Equation of tangent line to curve at a point We are given, y=13tan-1xwe know…

Q: Let f(x) = (sin x)³ + (cos x)³ 3 Enter the total number of critical numbers on the interval [0, 27].

A:

Q: 8.- Aright triangle with dimensions of X=3cm and y=41am if (x) is increasing at arate of 2cm / sec…

A: GivenIn a right angled trianglex=3cm, y=4cm   x is increasing at the rate of 2cm/secy is decreasing…

Q: = Suppose a company's revenue function is given by R(q) - q³ + 380q² and its cost function is given…

A: NOTE: Refresh your page if you can't see any equations. . revenue and cost functions are

Q: 2. Graph examples of functions y = f(x) (separate functions for each part) such that: (a) f(x) is…

A: (d) The tangent line to y = f(x) at the point (1,2) intersect the graph of f(x) at exactly three…

Q: Find h′(2) if h(x)= ln(x+√x^2-1) h'(2)=

A:

Q: Equations Linear in Two Variables 2. (2x+3y-1)dx + (2x+3y + 2)dy=0 x(3) = 1

A:

Q: A population of a particular yeast cell develops with a constant relative growth rate of 0.4265 per…

A: we need to find out the population after 4 hours.

Q: Exercise IV: Revenue functions Assume that the demand of chocolate of a local producer is given by q…

A: The demand function is:q=9-p

Q: en the following geometric series, answer the questions below: 20+ 18+ 16.2, (a) Explain why this…

A: Given query is is to find the sum of the series and creat a similar series.

Q: Consider the rational function f(x) a. Determine the vertical intercept of f. f(0) = b. Determine…

A:

Q: Find the interval of convergence for the given power series. n²(x + 6)" n=1 (2²) (n ³) The series is…

A:

Q: 4. For each function that is one-to-one. a) Find the inverse of the function, b) Graph fand f-¹ on…

A: (4). (a).The given function is:f(x)=2x+6x-3 ;       x≠3

Q: n=1 9 (3n − 1) (3n+2)

A: To find: ∑n=1∞93n-13n+2 ∑n=1∞9(3n-1)3n+2=∑n=1∞ 33n-1- 33n+2

Q: Test the series below for convergence using the Root Test. 3n + 5 n=1 (27 2n + 4 f(n) The limit of…

A:

Q: B. Solve the problems related to the application of First Order Differential Equations. 5. Mixture…

A: Question In an oil refinery, a storage tank contains 2000 gallons of gasoline that initially has 100…

Q: Let r(t) = (2t³/², cos(4t), sin(4t)). Find the equation of the tangent line at t = 0.

A:

Q: A drug response curve describes the level of medication in the bloodstream after a drug is…

A:

Q: Describe the domain of integration of the integral. [² √81-x² /81-x²-² xy dz dy dx Choose the…

A:

Q: A triangle has a base that is increasing at a rate of 2 cm/sec and a height that is decreasing at a…

A:

Q: 21. Use the first and second derivative rules from Section 2.2 to show that the graph of ye has no…

A:

Q: πρ 4. Show that the area of a circle sector with radius r cm and angle radians is 2 cm².

A:

Q: The graph of f(x) = 3 - 4 over the interval [0,2] is sketched below. Do you S (3-4) dx to be expect…

A:

Q: Using polar coordinates, evaluate the volume of the solid in the first octant bounded by the…

A:

Q: Suppose that the monthly cost, in dollars, of producing x chairs is C(x)=0.005x³ +0.07x² + 16x +…

A:

Q: 8. Given x+1 and g(x) = 1. find state its domain. (f+g)(x) and

A: Add f(x) and g(x) to find (f+g)(x)

Q: If a is an integer, then the function s is not continuous at point a. Explain.

A: If there exists a real number 'x' then it might be an integer or any irrational or irrational number…

Q: A se 0

A:

Q: (a) Suppose y = f(x) is an unknown function but that you know that f(4) = 11 and f'(4) = -0.18.…

A:

Q: can you redo this? 27 is incorrect.

A: Let y=3.75x4+1.25 and dxdt=0.2.To find dydt when x=3.

Q: Express the region D = {(x, y)|3x² + 3y² ≤ 45} in polar coordinates.

A: D=x,y|3x2+3y2≤45

Q: Consider the function f(x) = 2x³ + 3x² 120x + 5, -5 ≤ x ≤ 5. This function has an absolute minimum…

A:

Q: Suppose f(x, y, z) = x² + y² + z² and W is the solid cylinder with height 5 and base radius 5 that…

A:

Q: Assume that all variables are implicit functions of time t. Find the indicated rate. dy dt dt x +…

A: As we know from the Chain rule: dydx=dydt·dtdx And use the Power law: ddxxn=nxn-1   Given:…

Q: The points of intersection of the cardioid r = 1 + sin 0 and the spiral loop r = 20,-π/2 ≤ 0≤ π/2…

A: The given curves are cardioid r=1+sinθ and the spiral loop r=2θ, -π2≤θ≤π2.

Q: e equation of the tangent line to the graph of the function f(x) = (2+9) (-4) at the point (0, -36).…

A:

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interva as a…

A:

Q: Evaluate f (x - y)(y – z) dV for the box B with dimension: [3, 6] × [0, 5] × [0, 5]. (Use symbolic…

A: Given: The dimension of the box:B=3, 6×0, 5×0, 5

Q: The figure below shows a satellite orbiting Earth. The satellite passes directly over two tracking…

A:

Q: Express the region D = {(x, y)|3x² + 3y² ≤ 24y} in polar coordinates. Provide your answer below: D =…

A:

Q: I need help when it comes to trig identities. I'm having a hard time finding integrals of tan and…

A: A little bit of trigonometry (Basic transformations) and some pre-cal is required for such…

Q: The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the…

A:

Q: When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C…

A:

Q: Find all the critical values for the given function shown below. If there are not any critical…

A: