Find the limit (if it exists): In t (e¹i+ t² — I j lim t→1 O ei + 1-3 + cos(1)k O Does not exist 1 O ei + j Oi-j+k O ei + 2j + cos(1)k + costk)

Q: Find the indefinite integral. (Use C for the constant of integration.)

A:

Q: For approximately what values of x can you replace sin x by x- error of magnitude no greater than…

A: Given DataThe expression is x-xᶟ/6.The magnitude of error is 2×10-4.The expression for the expansion…

Q: Evaluate the following integrals using the Fundamental Theorem of Calculus: (a) fª e² da 0 b) * cos…

A:

Q: A rectangular beam will be cut from a cylindrical log of radius r =30 inches. Suppose that the…

A: We need to find dimension of the strongest beam.

Q: Let a = and b =. Find k so that a and b will be orthogonal (form a 90 degree angle). k=

A:

Q: 5) Let B(x, y) = 3x + 2y². Find the minimum and maximum values of B on the unit circle x² + y² = 1.

A:

Q: Sketch the graph of the function. (Select Update Graph to see your response plotted on the screen.…

A: x03.5y02.8

Q: Use the chain rule to find the indicated partial derivatives. Р+9 p+r aN ди aN av an = = N = ƏN ди…

A:

Q: The daily marginal revenue function associated with selling x widgets is given by R'(X) = 15x² + 12x…

A:

Q: Let a = 2j - 5k and 6 = 3i – 2j + 2k. Find −ā + 37. -ā + 3b =

A:

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

A:

Q: If tan (0) (a) sin(0) == (b) cos(0) (c) sec(0) (d) csc (0) (e) cot (0) = - = = = 5 and sin(0) <0,…

A:

Q: W = F(3t+2, 2t + 1) where F(u,v) is a differentiable function with F (2,1)= -3 and F (2,1)=5, find…

A:

Q: Compute the derivative. Use logarithmic differentiation where appropriate. 6 +9) X d dx X

A:

Q: Find the absolute maximum and minimum values of the following function on the given region R. f(x,y)…

A:

Q: Represent the function 5 (1-10x) 00 as a power series f(x) = c n=0 спаем

A: Use ratio test of the convergence

Q: 2. One minute after a 100-mg sample of Polonium-218 is placed into a nuclear chamber, only 80-mg…

A: Note:-Since you asked multiple question , according to our policy we can answer only first question…

Q: Find the slope m of the line that passes through the points (-10, 4) and (2, 4). Enter an exact…

A:

Q: A country's postal service will accept a package if its length plus its girth (the distance all the…

A:

Q: A rectangular campsite on the shore of a lake is to be surrounded on three sides by a narrow, 80-m…

A:

Q: y" - yy' + sy ( чу! = 2X (x+2) e sinx

A:

Q: Given a vector that has an initial point of (-3, 4) and terminal point of (2,-5), both graph the…

A:

Q: Find the parametric equation for the line where the planes 6x6y2z = 24 and 6x - 4y - 4z = 24…

A:

Q: I si sin? x cos3 xdx х

A:

Q: Solve the system of equations using Gaussian or Gauss-Jordan elimination. -x + y+ z= -4 -x+3y- 5z…

A:

Q: Let ƒ(x) = ln[x³(x + 4)¹(x² + 4)5] f'(x) = You need not put it over a common denominator.

A:

Q: Find the first partial derivatives of the function. R(p, q) = tan-¹(pq8)

A:

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A:

Q: 12. Find an equation of the normal line, the tangent plane of the surface (S): x² + y² − √√y + z² =…

A:

Q: cọ xdx 2 √x4-1

A:

Q: Let f(x): 1 + (a) For what value of c is f a probability density function? -1,1 C = (b) For that…

A: The solution is shown in step-2

Q: 3 Given x+y³ - 100y = 8, answer the following questions. a.) Find all values of y that correspond to…

A: Given: To Find:(a)  To find all values of  that correspond to .(b) To find the slope of the tangent…

Q: The estimated marginal profit associated with producing x widgets is given by P'(x) = -0.8x + 32…

A: The estimated marginal profit associated with producing  widgets is given by where   is measured in…

Q: (c) 0 ( cos (Tr) - sin (r)) dr

A:

Q: Let √√x²-16 y² y - 3 Sketch the domain of f on xy-plane f(x, y) =

A: Domain of a function is all the points or values for which a function defined.

Q: Find the unit tangent vector to the curve defined by r(t) = (3 cos(t), 3 sin(t), 5 sin²(t)) at t =…

A:

Q: Find the curvature of the function = cos(7лx) at x = -0.5. Curvature: Find the radius of curvature…

A:

Q: Find the number c that satisfies the conclusion of the Mean Value Theorem. Given f(x) = 2sinx +…

A:

Q: 4. In what direction is the function f(x, y) = x² + ln(x + 5y) decreas- ing most rapidly at the…

A: In what direction is the function f(x, y) = x ^ 2 + ln(x + 5y) decreasing most rapidly at the point…

Q: 1. Let y = f(x) be a cubic polynomial with leading coefficient a = 2 and f(-2)=f(1) = f(2)=0. find…

A:

Q: Find an equation of the plane tangent to the following surface at the given point. z=8-2x²-3y²;…

A:

Q: Find the slope (in reduced fraction form) of the tangent line to the curve −3x² - 2xy − 3y³ = −203 -…

A:

Q: How long will it take $4,000 to grow to $8,500 if the investment earns interest at the rate of 11% /…

A:

Q: I am seeing different answers for the same question, can you do it again properly and precisouly

A: This is the correct way of solving and solution

Q: If sin (0) = (a) cos(0) 2 , and is in quadrant II, then find > - 7 = (b) tan (0) = = (c) sec(0) =

A:

Q: Two chemicals A and 8 are combined to form a chemical C. The rate, or velocity, of the reaction is…

A:

Q: Estimate I I≈ 27 - L² (3x 0 (3x - 1a²)da using midpoints and n = 3 subintervals.

A: In this question, we will find the integral by using mid-point method.

Q: The masses m, are located at the points P. Find the moments My and My and the center of mass of the…

A:

Q: Truck Rental Company Y rents out a moving truck for one day by charging $25 plus $0.07 per mile.…

A: If the rate per unit is  then the rate per units is .

Q: For the following vector, convert from magnitude and direction to x and y coordinates r = 3, 0 = 20°…

A: