Check the fundamental theorem for gradients using the function T = 5sz (2+ sin²4) Pick as your path a quarter circle parallel to the x-y plane at z=a, starting at x=b and ending at y=b.

Q: dz dt If (z=x. y), where x = cos (t) and y = sin (t) 03. Use the chain rule method to find

A:

Q: aquar the aquarium. (Use Show how to approximate the required work (in J) by a Riemann sum. (Let x…

A:

Q: I.B. Sketch the graph of a function f satisfying ALL the given conditions. ● • f(-4)= -2 ● The…

A: Information                                             Graphical interpretation

Q: Given that f(x) = (x-7)2 and g(x) = 7 - 4x, find: a) (f + g)(-3)- b) (f-g)(-3)- c) (fg)(-3)- d)…

A:

Q: 3. Let k(x, y) = ex cos(x+2y). For any (x, y) € dom k, evaluate 2k(x, y) + 4ky (x, y) — kxy(x, y) +…

A:

Q: Find the open interval(s) on which the curve given by the vector-valued function is smooth. (Enter…

A:

Q: If f(x) ƒ'(x) = | = 4x sin cos x, find Find f '(1) =

A:

Q: Find a and b so that f(x) = 2x+1 + ax² + bx+ 2021 satisfies the following: ● ● The average rate of…

A:

Q: Average cost.  Tongue-Tied Sauces, Inc., finds that the cost, in dollars, of producing x bottles of…

A: Cost function C(x) = 375+ 0.75x^(3/4) Then find the rate at which average cost is changing?

Q: ( xy² + y ² ) dy = ( x ³ y ³ + x² - y ³-1)dx

A:

Q: Find the limit of the following:  a) lim x→∞ (1 - x2 / x3 - x + 1) b) lim x→∞ (x - x√x / 2x3/2 +…

A:

Q: Evaluate each limit, if it exists: x²-4 a)lim 22-4 X-2 1-x² b)lim x-1 1-x x²-4x x-0 x(x-1) c) lim

A: Here we have to find the limit of the functions.

Q: Let f(x,y,z) = x²-tany² 2xyz Solve for fzxy.

A: Given :fx,y,z=x2-tany22xyz

Q: 5. Y=√√4x+ 3

A:

Q: Use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = -2x³ f(x)=

A:

Q: ood to go Evaluate the integrals S√4x²dx 2. S 1 (4+x²)² dx

A:

Q: Q2/A: Find the Fourier Series of the function : f(x) = X + π_if - π< X < π and f(x+2n) = f(x)

A: Fourier series of a function is given by f(x)=a0+∑n=1∞ancosnπxM+bnsinnπxM    for -M≤x≤M.Where,…

Q: Let x represent the units of labor and y the capital invested in a manufacturing process. When…

A: The solution consists of differentiation of equation with respect to x

Q: Q3/ A: Find General Solutions for the following Differential Equations (Use Differential Operators).…

A:

Q: If p is the current frequency of the resistance gene in a model for the spread of drug resistance,…

A: We need to find the value of  limp -&gt;19p2-2pp2-2

Q: Which of the following is NOT a part of Quantitative Analysis?   a. Logic b. Weather c. Historic…

A: a. Logic - Logic is an analytical philosophy. b. Weather - Weather is a quantitative analysis…

Q: Evaluate_lim_ (√√9x² − 5x +1 + 3x 3x). -

A:

Q: 14. Find f'(x) using the limit definition of the derivative. 3x x+1 f(x)=

A:

Q: If f(x) = ƒ'(x) = 4x(sin cosx), find

A:

Q: Suppose that 4 J of work is needed to stretch a spring from its natural length of 24 cm to a length…

A:

Q: Calculus Two surfaces are said to intersect perpendicularly at a point if their normal vectors are…

A:

Q: If f(x) ƒ'(x) = = Cos = ƒ'(2): = 2 tan , then

A:

Q: Consider f(x) defined as follows: f(x) = 5x² + 13x + 6 |x + 2| [4 - 3x] + x, " x < -2 x ≥ −2…

A:

Q: X x + 5 Give exact answers (not decimal approximations). Let f(x) = Find the values of where f'(x) =…

A:

Q: Let y=e¯*(Acos(x) + Bsin(x)) be the solution of the initial value problem for the differential…

A: As 'y' is the solution of the differential equation , so it satisfied the given initial conditions.

Q: 9. x², Let f(x)=sin(x), x < 0 0≤x<π/2 x-π/2, x≥π/2 (a) Graph f. Your graph should be accurate with…

A: See this solution in below.

Q: Given f (x) below, select ALL of the true statements. lim-4+ f (x) = 1 lim, 4 f (x) = 1 lim,-4-f(x)…

A:

Q: * 1. Apply the limit function to determine the derivative of y=√x - 1 Your answer

A: Please see the below picture for detailed solution.

Q: 2. A circular walkway is to be built around a monument, with the monument as the center. The…

A: Given Coordinates of the monument (0,0) Distance of any point on inner boundary from the monument is…

Q: lim 8个8 5x 2x² +9

A: To find the limit of given function.

Q: Solve the problem. The population P of elephants in a wild animal preserve changes with time (in…

A:

Q: A tank initially holds 200 gal of brine solution containing 3 lb of salt. At t=0, another brine…

A:

Q: Decide if each set of inequalities provides sufficient information to determine lim f(x), and if it…

A:

Q: The condition is, H (7) = 17.9; 260 1+ Ce-0.004 (7) 17.9= ⇒1+C₂-0.004(7) ⇒Ce-0.004(7) 260 17.9 -662)…

A: a differential equation is an equation with one or more derivatives of a function. The derivative of…

Q: evaluate the determinant, given that a b de c e f h i 9 '|| -6

A: We know that if all element of any row is added to the corresponding element of any other row then…

Q: Find the limit of the following:  a) lim x→∞ (sin2x / x2) b) lim x→∞ (x - √x) *please do in hand…

A:

Q: Determine f'(a) for a = 2.5, 4, 7. 5 4 3 2 1 y 1 234 567 89

A:

Q: Find the solution to the given (y+x³y³)dx+xdy = 0₁

A: y+x3y3dx+xdy=0

Q: 1.) dy dx 2x-y² 1+2yx = 0

A:

Q: The total cost (in dollars) of manufacturing x auto body frames is C(x) = 70,000 +900x. (A) Find the…

A:

Q: The half-life of freshly-baked brownies at your house is 18 hours. If 200 brownies were present…

A:

Q: Q4. B. Find the tangential vector (T), normal vector (N) and binomial vector (B) for the position…

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

Q: 2) Suppose that f(x)=x*(1-x) Find the maximizing value of x and what f(x) equals at that x. b) How…

A:

Q: sin cos 0 cos sin

A:

Q: A || [3 2 4 2 3 0 2 0 -2 1-3 0 3 2 57 10

A: