Find the limit 11x³y lim along two different paths. No decimal entries allowed. (z,y) → (0,0) 3x6 + y² Along the path y = Along the path y = 11x³y lim (z,y) → (0,0) 3x6 + y² 12x³: 11x³y lim (z,y) → (0,0) 3x6 + y² 11x³y lim (z,y) → (0,0) 3x6 + y²

Q: Use logarithmic differentiation to find dy/dx. x² - 64 x² + 64 dy dx y = X>8 128x (x² - 64 ) ( ² )…

A:

Q: Find the work done by F= (x² + y)i + (y² + x)j + ze²k over the following paths from (5,0,0) to…

A:

Q: Suppose an arrow is shot upward on the moon with a velocity of 51 meters per second, then its…

A:

Q: 3. Consider the following parametric equations. x = (t + 1)² ; y = t + 2; -3 ≤ t ≤ 3 a. Create a…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. kindly repost…

Q: Use trigonometric identities and algebraic methods, as necessary, to solve the following…

A: 4cos2(x)+4=6

Q: How would you obtain the real and imaginary part of the following function: F(z) = e²?

A: Real & Imaginary part of the function, F(z) = ez.

Q: A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a…

A:

Q: 1. Evaluate the integral using substitution. TC/3 π/6 cos*x sin x dx

A:

Q: 2. The acceleration e²t - 25 of a particle at time t > 0 is given by a(t) + 2. Given that the…

A:

Q: a) The Metal Can Company has an order to make cylindrical cans with a volume of 250 cm³. What should…

A: Let us take the dimensions of a cylinder with the height h and the radius of the base r, we also…

Q: For the following composite function, find an inner function u = g(x) and an outer function y=f(u)…

A: To find out the inner function and outer function and also the derivative of the function with…

Q: v(t) = 5 sin(t) — 4cos(t); _s(0)=0

A: We know that the velocity formula v(t)=ds/dt

Q: Evaluate the following definite integral. Express your answer in terms of logarithms. €² dx 2 1…

A:

Q: 7. The width of a rectangle is decreasing at a rate of 1 cm/s and the length is increasing at a rate…

A:

Q: ← dy Find for the following function. dx dy dx 5 cos x y=8-9 cos x 11 40 sin(x) (8-9 cos(x))²

A:

Q: Use the intermediate value theorem to show that the polynomial function has a zero in the given…

A:

Q: A particle moves with a velocity of v(t) ft/s along an s-axis. Find the displacement and the…

A:

Q: (2) Let R be the region enclosed by the curves y = x² - 2x and y = x+4. (Note: one of these curves…

A: The given curves are: y=x2-2x       and      y=x+4

Q: Rate oil is pumped out (millions of barrels/month) -Select- Select- 40 35 30 Use the graph of r(t)…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: 2x + 5 3x + 3 Consider the function f(x) function there are two important intervals: (− ∞, A) and…

A:

Q: use a test of convergence to determine if the follow series converges or diverges: summation where…

A:

Q: Sales analysis. The rate of change of the monthly sales of a newly released football game is given…

A: The rate of change of the monthly sales of a newly released football game is given by  S'(t)=…

Q: The rate of depreciation (in dollars per year) for a certain truck is given by the function below,…

A:

Q: has two solutions. The smaller is 22x5×2x+6=0 and the larger is

A:

Q: 37. (6x² + 2) dx S x² + 2x - 3

A:

Q: cises 5–12, calculate MN and TN for the value of N indicated.

A:

Q: dy Use the Fundamental Theorem of Calculus to find where dx dy dx || cos (1x) ⁹ + sin x 1x…

A:

Q: Use a change of variables or the accompanying table to evaluate the following indefinite integral.…

A:

Q: 10. Find lim n→∞ n-3 n+3 4n

A:

Q: For the function, do the following. f(x) = 2x from a = 4 to b = 5 (a) Approximate the area under the…

A: The given function is: f(x)=2x   from a=4  to  b=5

Q: Question 11 2x cm 3x cm b) Show that the volume of the cuboid, V, is given by h cm NOT TO SCALE…

A: Figure 2 shows a cuboid of length 3x cm, width 2x cm and height h cm. The sum of the lengths of all…

Q: Find the mass and center of mass of the lamina that occupies the region D and has the given density…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: se Heron's formula to find the area of the triangle with side lengths 8, 17, and 20, as shown below.

A: Triangle with side lengths 8, 17, and 20By heron's formula = ss-as-bs-c

Q: 8. Section 7.6 a. Use the differential df to estimate the change in f(x,y) when x changes from 1 to…

A: We have given a function f(x,y) = x2y + 2xy3

Q: Is (r¹ + 13x² - 14) + (x² − 1) in Q[x]?

A: Since we are given with the multiple number of question and our guideline is solve first question

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: We have to find the distance travelled and length of curve. First let us find the derivatives of x…

Q: 1. A tower is 500 m tall. A ball is thrown downward at an initial velocity of 2 m/s. The height of…

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) 1 9 arctan(5x) +C 45 1 + 25x²…

A:

Q: 31. (a) Sketch an accurate graph of the cosine on the domain (-27, 27). Use this to sketch an…

A: We have to draw the graphs of the following

Q: a) For event A, P(A) = TT Write down P(A'). Give your answer in terms of . b) In a group of 13…

A:

Q: Find or evaluate the integral by completing the square. (Remember to use absolute values where…

A:

Q: Given the points: P(3,4,-1), (2,8,4), R(1,3,-5) a) Find an equation of the plane containing all the…

A:

Q: Find a polar equation for the curve represented by the given Cartesian equation. xy = 7

A: xy=7

Q: y = 4 cos(x), y = 8x² - 2

A:

Q: Looking for someone to verify my problem solving. I graphed a region bound by y=1 and y=x^3. If I…

A:

Q: A manufacture has been selling 1500 television sets a week at $390 each. A market survey indicates…

A:

Q: 1. Sketch a graph of a function f that is differentiable and that satisfies the following…

A:

Q: Suppose a product's profit function is given by 7q² + 700q, where (9) is in dollars π(q) and q is…

A:

Q: find the radius of convergence of the series x^n/n+1

A:

Q: Consider the function f(x) Let F(x) be the antiderivative Then F(2) = 5 4 x4 x6 of f(x) with F(1) =

A: