Evaluate the following limit: lim, 2 (2 6²5-6 2y³-5y³+5y-6 1/3 7/9 00 -2/5

Q: Evaluate the integral: - 17 L2V2² - dx x²√√√x² +9

A: Given, ∫-17x2x2+9dx

Q: Suppose a company has fixed costs of $33,600 and variable cost per unit of x + 222 dollars, where x…

A:

Q: Use implicit differentiation to find az/ax and əz/ay. xy²z³ + x³y²z = x+y+z

A:

Q: 1. y = x³ (sin(lnx) - cos(lnx)) 2. y = ln 1+sinx 1–sinx (use properties of logarithms)

A:

Q: a. Find the inverse of ƒ(x) = -x + 1. Graph the liney = -x + 1 together with the line y = x. At what…

A: Concept used: Inverse function An inverse function that reverses into another function is called an…

Q: 4. y = x²(cos(lnx) — sin(lnx))

A:

Q: Find all vertical and horizontal asymptotes. 101 y 5- -10- Vertical Asymptote(s) Horizontal…

A: A vertical asymptote is a vertical line along which the function goes towards infinity or -infinity.…

Q: 1. Express the given function H(x) as a composition of two functions f and g such that H(x) =…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Compute the first-order partial derivatives of the function. w = In (x7 — y4) (Use symbolic notation…

A:

Q: 2 lim √√9-x² - y² (x,y) →(0,0)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: d) How long is the ball above a height of 10 m? e) How long is the ball in flight?

A: We have to find time for which the ball is in flight.

Q: = = '1' (a) 21 = 6e-i (b) z2 = 21, (c) 23 (d) z4 = 21 + Z2, (e) 25 = 21 - 22. 2122, 2п 3

A: We have given some complex number problems in Euler's Form. We have find the real and imaginary…

Q: Find the indicated derivative. f'(8) = If f(x) = 3 6x2 48 3 find f'(8). VX

A: Given query is to find the derivative.

Q: f(x) = x²(3x) on [-3, 5] solute min solute max

A: Topic:- application of derivatives

Q: 19. The graph of f is shown to the right. For which value of x is f'(x) the smallest? [A] x=6 [B]…

A: given graph of f(x)

Q: What happens if you take B = A in the trigonometric identitycos(A - B) = cos Acos B + sin Asin B?…

A: The given identity: cos(A - B) = cos Acos B + sin Asin B To check what happens if B = A .

Q: State the limit or sum of limits of proper integrals that must be evaluated in order to determine…

A:

Q: 1. Compute the three partial derivatives of f(x, y, z) 1 (x² + y² +2²)n

A: see below the answer and calculation

Q: Solve the ff. first order DE using Exact Equations a. (x + y)dx + (x − y)dy = 0 - b. (y² − 2xy +…

A:

Q: Compute the first-order partial derivatives of the function. z = tan (3uv4) (Use symbolic notation…

A: We have to find the partial derivatives.

Q: 2. xdy-√√x² + y²dx = 0

A:

Q: 22. Throwing a baseball A baseball is thrown from the stands 32 ft above the field at an angle of…

A: We will use formula for horizontal range and total time of flight.

Q: (²-5) 69. lim 1 (x,y) →(2,5)

A:

Q: Find the equation of each hyperbola whose center is at the origin. Find the equation of the…

A:

Q: x+2 2x²+5x+2 11. Find all x values at which f(x) discontinuity and redefine the function to make it…

A:

Q: y = f(x) +7 Vertical asymptates horizontal asymptotes oblique asymptotes Domain of of f

A: We have to find the asymptotes and domain of function.

Q: Now, the given DE is of the form Mdx + Ndy = 0. M = 4x³+1 and 2N = 4x³ +1. ду ax So, 2M = ON,…

A:

Q: Evaluate the integrals. Making use of trigonometric Substitutions. dx x²-√2²-x²

A: We need to solve the following integral I = ∫dxx2a2-x2                             ............1

Q: 5) consider the indefinite integral [cos ³ (x) dx. Explain why the Substitution U = COS (x) will not…

A:

Q: Find the derivatives a) f(x)=√x+1 b) f(x)=sin(x+3) at a=0 c) f(x) = == X x+1 of the following…

A:

Q: Find an equation of the tangent plane to the parametric surface R(u, v) = = ㅠ at the point where u =…

A: Partial derivative and vector calculation are required

Q: Solve the ff. first order DE using Homogenous Equations. C. 3(3x² + y²)dx - 2xy dy = 0

A:

Q: Are (-7,6,4,-8) and (-35,30,20,-40) homogeneous coordinates for the same point in R³? Why or why…

A:

Q: If f(x) = (4x² + 5)5/2, compute the first and the second derivative of f(x). f'(x) = f"(x) =

A: Given query is to find first and second derivative.

Q: e the Chain Rule to compute the partial derivative. d -In (6u². + uv) = 0 du Orrect

A: Topic :- Application of derivatives

Q: differential equations  Solve the given initial-value problem. 5y'' + y' = −8x,  y(0) = 0, y'(0) =…

A: Solution of a initial value problem is given by y(x)=yc(x)+PIwhere, yc(x) is the complementary…

Q: Find d2y/dx2 if x = 3 - 2z and y = z2 - 3z3

A:

Q: e* (sin y - sin x + cos x) dx + e*(siny + cos y + cos x)dy = 0

A:

Q: A projectile is shot upward from the surface of Earth with an initial velocity of 127 meters per…

A:

Q: locate the local maximizers and local minimizers. Don't forget to account for endpoints! imizers…

A: We need to find local max and min of given function.

Q: lim (z,y) →+(π/4,1) y tan z 3+1

A: See the details solution in below

Q: In Exercises 57-64, solve for t. 57. a. e0.3t = 27 b. e = c. In02 = 0,4 %3D 58. a. 0.0l = 1000 b. c.…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A:

Q: A thermometer is taken from a room where the temperature is 23°C to the outdoors, where the…

A: Explained below

Q: In Exercises 39–42, express the given quantity in terms of sin x and cos x. 39. cos (7 + x) 40. sin…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: v2 dv

A:

Q: 7. Sketch the vector field F = (x − y)î + yĵ. Identify where F₁ vanishes. Identify where F2…

A: According to our guidelines,i can solve only first please reroute the remaining question.

Q: Find the derivative of y = 1+1=10 17 Or=0 + 30 3 Oy= Oy=- ▬▬ + 17 - 17 4 (3-17²) 33

A: y=3-17x23x3

Q: Match each function f with a function g so that (fog)(x) = x². (x² + 2)² (²-2)² x² - 2x + 1 :: 2 ln…

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

Q: 1. x²sin (y) dx - cot(y) dy=0

A: