Find the equation for the line tangent to the parametric curve: at the points where t = 4 and t = -4. For t = 4, the tangent line (in form y = mx + b) is y For t = -4, the tangent line is x = t³ - 16t Y 16t² - 14 =

Q: Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and…

A: Here

Q: Find the indefinite integral of the function g(x)=e^(2x) sin(3x)dx

A: The objective of this question is to find the indefinite integral of the function g(x) = e^(2x)…

Q: Determine the critical numbers, if any, of the function f. f(x) = 3x² + 3x³ - 54x² - 81x + 21 Give…

A:

Q: A company's marginal cost function is C'(x) = 686 - 4x +0.06x² where x is the number of units, i…

A:

Q: Use special limit rules to discuss your response, you may use any graphing tool to support your…

A: In a n-sided regular polygon, the angle made at the center is the division of the total angle of a…

Q: Give equation

A:

Q: 8. Find the linearization L(x) of f(x)=√√x² +9 at x = -4.

A: Given that the function

Q: Minimizing Heating and Cooling Costs A building in the shape of a rectangular box is to have a…

A: We have to find the dimensions of the building that will result in a minimal annual heating and…

Q: Use the information to find and compare Ay and dy. (Round your answers to four decimal places.) y =…

A:

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 4zi +…

A: We have to find the flux of the curl of the field F using surface integral in Stoke's Theorem.Given…

Q: Consider the following parametric curve. Answer parts a and b. 70 x=2 sint, y = 2 cost; t=2 a.…

A: The given parametric equation of curve is

Q: Let h(u) = (u +3) (u - 4) Determine the most general antiderivative of h. (u +3)(u — 4)du = -

A: Given,

Q: Find the sum of the series: n=0 (-1)"49"+2 n!

A:

Q: Let f(t) be the function 2t² + 1t+5. Follow the steps below to use the formal definition of the…

A: Let  be the function .By using the formal definition of the derivative .

Q: 4. n=1 ne-n

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: f(x) = cos² (3x + 1) − sin² (3x +1) f(x) = ln 1-sin 2.7

A:

Q: Hello, I need to evaluate the limits below but the grahp is made on paint, sorry about that.…

A: Given graph of function

Q: Match the series with the right expression. (Use the Maclaurin series.) (−1)n3−(2n+1) 2n + 1 1. 0 2.…

A:

Q: Find the dimensions of the right circular cylinder of greatest volume that can be inscribed in a…

A: The right circular cylinder is inscribed in a sphere of radius .The aim is to find the greatest…

Q: 1) Write a complex number in a standard form z = x + ly:: 2+i (2- i)(3i+ 4)(i+1)

A: The given complex number is

Q: Evaluate the integral: 16 √ 2² √² + 64 0x = (A) Which trig substitution is correct for this…

A: We have to evaluate the integral using trigonometric substitution.

Q: Compute the electric charge on the surface which is the portion of the cone z = √√3x² + 3y2 in the…

A:

Q: 3. Which of the following statements about the function y = f(x) graphed here are true, and which…

A:

Q: 9. The angular displacement of a spinning shaft is given as = 0.7t² - 5t+3, where is in radians and…

A: Given that the angular displacement of spinning shaft is where  is in radians and t is in seconds

Q: The Taylor series for f(x) = e² at a = 3 is Σen(x − 3)". n=0 Find the first few coefficients. Co C1…

A:

Q: Use the identity 2 sin æ cos x = sin(2x) to find the power series expansion of sin² x at x = 0.…

A:

Q: ind the surface area of the portion of the bowl z=9+x^2+y^2 that lies below the plane z = 13.

A: The formula to find surface area of 3D region is

Q: Let h(z) -5+42-42³ 2² Determine the most general indefinite integral of h. I -5+42-423 22 dz P

A:

Q: Simplify the following complex fraction; State the domain restriction: 1 X|N 2 1 1 X 1 -

A: To simplify the following complex fraction. To state the domain restriction.

Q: Find the equations of the tangent and normal lines to the graph of the function at the given point.…

A: The equation of the tangent line  to the curve y= f(x) at x= a is  The equation of the normal line…

Q: Find the Taylor polynomial of degree 3 of the function f(x) = arctan(9x) at a = 0. T3(x) = ||

A: f(x)=arctan(9x), a=0

Q: 16. You are designing a rectangular steel vat with a square base, an open top, and a volume of 32…

A:

Q: If sin(-s) = 5/13, and (a) (b) (c) (d) sin s cos(-s) COS S 3πt < s < 2π, compute the following.…

A:

Q: Simplify the following rational expression. State the domain restrictions: a) b) x³-8 2x3-8a 9-x²…

A: Given two rational functionsand,.We need to find the domain restrictions.

Q: 1 se sec4 x tan x dx

A:

Q: 4-Z 4-z-2y k √ ₁² √²-²² ² -² -²y xyz²dx dy dz = 1 2 0 0 0

A: To solve for unknown.

Q: The table shows the total assets (in trillions) held in a foreign bank for the given years. Complete…

A: We have to find the function using table values

Q: Given the ellipse : 1 (x+2)² + (−1)² = 9 4 (a) Graph the ellipse, together with its major and minor…

A: The blue dashed line represents the horizontal and vertical lines passing through the center.

Q: Use calculus to show that if f(x) = (x − a)²g(x), where both f(x) and g(x) are polynomials, then…

A:

Q: x = 2. (a) lim Below is the graphs of f(x) and g(x), and their tangent lines at YA y = 1.8(x-2) 0 x…

A:

Q: 3. Sketch these functions and find their domain and range. a) f(x) = √√3x b) y = x³

A:

Q: Find the derivative of the function. y = 7x-6 8x+3

A:

Q: 5 1 - 9x Compute the first few coefficients of this power series: Represent the function -Co C1 C₂…

A: The given function is 5/(1-9x).

Q: 15. An open rectangular box is to be made by cutting equal-sized squares from the corners of an 8"…

A: The dimensions of the box are:Length: L=15-2xWidth: W=8-2xHeight: H=x

Q: 2. S x³ +1 x³ - x² da dx

A:

Q: 17. What are the dimensions of the right circular cylinder of greatest volume that can be inscribed…

A:

Q: Let f(x) be a continuous function for which we know f(2)=3, f(4) = 5, f'(2) = 7, and f'(4) = 19.…

A:

Q: The marginal profit in dollars on Brie cheese sold at a cheese store is given by P'(x) = x (20x²…

A: The given marginal profit function , where  is the amount of cheese sold in hundreds of pounds.The…

Q: (t²-2t)³ 5t 4. The voltage applied to a 0.25-F capacitor is given by v=- 3.7 s. . Find the current…

A:

Q: S (x² − 2) dx; n = 4 32.

A: