If lim f(x) exists, then f is differentiable at x=c. X-C True False

Q: dx z/L1(zx — 6) вх І

A: The given integration is: ∫x149-x2172dx

Q: Suppose the function y = f(x) is defined by an equation x² + y² + sin(xy) = 9. Given that f(0) = 3.…

A:

Q: Use a trigonometric substitution to calculate a non-zero constant. X √x² + 2ax dx, where a is

A: The given integration is: ∫xx2+2axdx Use a trigonometric substitution to find the value of the given…

Q: Use spherical coordinates. Evaluate e /f/ ²₁ z dv, where E lies between the spheres x² + y² + z² = 9…

A:

Q: h. Simplify the function t In 2 N(t)= Noe h, to show that the function can be written in the form…

A:

Q: Suppose that R is the finite region bounded by y = x, y = x + 1, x = 0, and x = 3. Find the exact…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y = 3x², x = 1, and y = 0,…

A:

Q: Given f(x) f(x) = ln (√x² + 3) find f'(x) f'(x) =

A:

Q: Find the x-value where the maximum value of y = sin(x) - 4x² occurs using Newton's Method. Round…

A:

Q: For the function f(x) given below, evaluate lim f(x) and lim f(x). x-x X118 Provide your answer…

A: Given query is to find indicated limits.

Q: Find the most general antiderivative or indefinite integral. [(e-11x + 2x) dx S(+2) - 11x dx =

A:

Q: sample of mold in a Petri dish was found to grow at a daily exponential rate. In 3 days, the sample…

A: Given query is to find rate of growth.

Q: The volume of a cylinder with a radius of 5 inches is increasing at a rate of 367 in ³/min. How fast…

A: Given, r= 5inches volume is increasing, dV/dt = 36π in3/min h= 10 inches  Radius is not changing so…

Q: For the function f(x) = -7x² + 9x + 4, find the equation of the tangent line at x = 4.

A:

Q: Bernoulli's equation dy dx -ye-2x = 6y8, will be reduced to a linear equation by using the…

A:

Q: (P) xp- (e) fx dx (1) √(2x² - 6² xp(x9

A:

Q: Find the volume of the solid generated when the region bounded by y = 7x and y=21√x is revolved…

A:

Q: A polynomial f (x) has the given zeros of 8, –1, and –3. Part A: Using the Factor Theorem,…

A:

Q: Prove the following about limits of functions. 1. If f(x) = 3x - 1, then limx→4f(x) = 11. 2. If…

A:

Q: A window is composed of a semicircle placed on top of a rectangle. If you have 40 feet of…

A:

Q: Find the relative maxima and relative minima, if any, for the function f(x) = (x − 1)²/3 — (x +…

A:

Q: The annual average price per r foot for office space in a city was $30.89 in 2004, and it was $06 55…

A:

Q: 2. y = 2√x-x Curve Sketching Information Domain Intercepts Local maxima Local minima Point (s) of…

A: Note: - According to the company policy we can attempt only three subparts of a question so please…

Q: 1. Find the critical points of f(x), the intervals on which it is increasing and decreasing, and…

A: f(x) = (k - bx) ex  Roots of the function, f(x)= 0 (k - bx) ex = 0 ex cannot be equal to zero.…

Q: If f(x) √² (2³. (t³+3+²+4)dt

A:

Q: Use the Laplace transform to solve the given initial-value problem. y" — y' = et cos t, y(0) = 0,…

A:

Q: The degree of homogeneity of- (A) Not Homogeneous B O – 1 1 2 √x² + y² y²-3xy + 2x² D 1 is

A:

Q: State the domain, vertical asymptote, and end behavior of the function. Enter the domain in interval…

A: Please see the below picture for detailed solution.

Q: a. Write a function F(t) that describes the value after t years of a $2000 investment that increases…

A: need to write down the given information as a function.

Q: f(x)=3x2+2x-5 g(x)=x2+7x-2 7 A BI

A: Given query is to solve the system of equations.

Q: If f(x)=x²-x²+-, then/"(2) =

A:

Q: Calculate the double integral. x sec²(y) dA, = {(x, y) 10 ≤x≤ 2,0 ≤ y ≤ }

A:

Q: If f(x) = x²√√3x+1, then f'(x) A B с D -9.x² + 4x 2√√3x+1 15x² + 4x 2√√3x + 1 9x² + 2x 3x+1 -3.x² -…

A: To find f'(x)

Q: Suppose that the cost, in dollars, for a company to produce x pairs of a new line of jeans is…

A: Given the cost functionC(x)=6500+6x+0.01x2+0.0002x3   We need to finda.Marginal cost…

Q: 4. 5. 6. Solve (-5+91)/(1-i) Solve (5-41)/(-2+6i) Solve (3+5i) - (11-9i)

A: 4)-5+9i1-i

Q: Show that the point of intersection of two lines in the plane of afield F lies in the plane of F.

A: Point of intersection:- The junction of two lines is referred to as the point of intersection. The…

Q: Determine the maximum area of a rectangle inscribed in the ellipse include any units. Provide your…

A: To determine the maximum area of a rectangle in the ellipse x264+y281=1.

Q: Use spherical coordinates. Find the volume of the solid that lies within the sphere x² + y² + z² =…

A: Given Sphere is: x2+y2+z2=25 and Cone is : z=x2+y2

Q: Q4. Evaluate the limits of the following functions as x → 0 sin² x x² (a) f(x) = e (b) f(x) = x ln…

A: L'Hospital rule:- If a function f(x)=p(x)q(x) has the limit 00 form then limx→0f(x)=limx→0p'(x)q'(x)…

Q: Which of the following set(s) of ordered pairs represents the solution to the system of equations…

A:

Q: Make a sign diagram for the derivative of the function f(x) = x3 - 3x2 -24x+7 including all open…

A:

Q: Newton's Method will fail to approximate the solution to f(x) = 0 with initial guess ao when: ao is…

A: We need to choose correct option.

Q: Consider the function Evaluate the following (a) f(5) (b) f(x) + f(5) (c) f(x-2) 3 f(x)=2x² +9x+3.

A:

Q: Determine whether the following integral converges or diverges. π 2 So² cos (0) de √sin (0)

A: Given query is to find integral converging or diverging.

Q: Consider the double integral L = 1+2²³ + y² dy dz. (a) Sketch the region of integration for the…

A: Let's sketch the graph and evaluate double integral.

Q: Use differentials to approximate the quantity. (Round your answer to four decimal places.) √28

A: Given quantity is 283 We need to find its approximate solution using differentials

Q: Identify the modal (mode) sport from the survey results. Calculate the number of learners that chose…

A: All the subparts are solved below:

Q: Consider the following function. h(x) = x-1¹/3(x-8) Find the derivative of the function. h'(x) = X =…

A: we need to find out the derivative h'(x).

Q: If f(x) = then f'(x) = f'(3) = t³ dt

A:

Q: (b) Use the gradient to find the directional derivative Du f(x, y) of f(x, y) = 9xy² + 4x² at P =…

A: