Differentiate the following function. f(x) = -3e-3x d -(-3e-³x) = dx

Q: 1. The population of a town grows at a rate of r(t) = 300 e0.2t people per year (where t is the time…

A:

Q: Use linear approximation, i.e. the tangent line, to approximate 101 as follows: Let f(x) = = and…

A: We need to find value using linear approximation.

Q: Consider the following graph. y 5A 3 y = 5 (arcsin (x)) 2 A H 2 -1 1 2 2 3 3 2 Given the function y…

A:

Q: Find the area of the surface obtained by rotating the curve from x = 0 to x = 5 about the x-axis.…

A:

Q: There are 3 red, 4 green, 4 white, and 5 blue marbles in a bag. If you select 2 marbles, what is the…

A:

Q: A car wash firm calculates that its daily production (in number of cars washed) depends on the…

A:

Q: 2 n (2k + n)2 k=2

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: 5. A ball of mass 2 kg is dropped from rest in a viscous fluid, the resistance of which is 0.001v N…

A: By solving differential equation

Q: Jse the definition of derivative to find f'(x) where f(x)=√x

A: Given,  f(x)=x

Q: Find the volume of the solid obtained by rotating the region B about the line y = -1. A B

A:

Q: Joseph completed the two problems, asking him to explain if there is enough information to prove the…

A: Given.

Q: A 170-foot tall antenna has 4 guy-wires connected to the top of the antenna, and each guy-wire is…

A:

Q: Given a > 0, evaluate the following limit: k X lim x-0 a 1x

A:

Q: (B): Find the integration by using substitution method [x√2x - 1 dx

A:

Q: 4 fsin 2xcos²2xdx

A:

Q: Given the function  y = 5 arcsin(x),  find  y'.

A:

Q: All exponential functions can be written in many forms. Write the function -0.08t f(t) = 340e- in…

A:

Q: Evaluatef (cot2x + 2tan²x - 5) dx a. cotx + 2tanx + 4x + C b. -tanx-2cotx - 4x + C c. -cotx 2tanx -…

A: I have stated the used formulas in the solution

Q: Q 19 If a fault cuts three sides of a quadrilateral, then: Red with one of the vertices 2- Cut the…

A: Given question:- 19) if a fault cuts three sides of a quadrilateral then,

Q: fferential Equations: Growth and Decay Answer the given problem. Show your solution completely with…

A:

Q: 7. f(x, y) = √x² + y²

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

Q: 1.₁-1/dt 2. -1 -2es-1ds

A:

Q: One car leaves a given point and travels north at 40 mph. Another car leaves 1 HOUR LATER, and…

A: Let's find rate of change distance between the cars changing at the instant the second car has been…

Q: Find the tangent line approximation for √1 + x near x = 5. y = |

A:

Q: 2.(D5 – 2D³ – 2D² – 3D — 2) y - - = 0

A: To solve the higher order differential equation.

Q: J 7+6x - x²dx

A:

Q: The acceleration of an object (in m/s²) is given by the function a(t) = 6 sin(t). The initial…

A:

Q: T 4.) x² sin(xy) dydx

A: Solve the following integrals.        ∫0π∫01x2sin(xy) dydx

Q: B. Solve the following integrals. 2.) fevdxdy

A:

Q: 2. Find the value of 1 3x + 13 x² + 4x +3 dx

A: We can you valve the given definite integral by using the partial fraction method.

Q: 7. Use contour integration to evaluate (a) dr x²+x+1² de (b) 3+2 sin

A:

Q: 10. Evaluate cos x sin² x dx

A:

Q: Find the derivative of the trigonometric function. y = cos((?x)8)

A:

Q: (a) Find if x² + y² + xy =1 dy dx (b) Identify the nature of the stationary points of y=4x³ - 21x²…

A:

Q: to evaluate the following: f(t³-4t² + 5t+ 32) sin(t)dt (B) Use Tabular integration

A: Given integral is :

Q: the volume of the solid B that lies above the cone z = √3x² + 3y2 and below the sphere x² + y² + z²…

A:

Q: 1. 2²₂(3x-4)dx

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

Q: Determine whether the differential equation (5x² - 2xy + 6) dx + (7y² − x² + 5) dy = 0 is exact. If…

A:

Q: fcos³ xdx from a = 0 to b = 3. 2

A:

Q: Calculate the partial derivatives at (T, U, V, W) = (4, 1, 5, 10). (Use symbolic notation and…

A: We can find the partial derivative of the given expression .

Q: X hat is the value of lima f(a)-aƒ(x)? r-a

A: Topic:- limits

Q: Q1/ Find the derivative of the following functions: where x>0,x #1 a- y = x** x√√2x+1 b- y = exsin…

A:

Q: Find all values of k, if any, that satisfy the equation. Enter the exact answer(s). 4 0 [22 k 40 = 0…

A:

Q: -: Show that -1+i√3 =1 for all combination of signs.

A:

Q: Find closed Sets A= [2,5), B = {2, 4, 6, 8, 10,--- }, C = {6, 21, 42, 58}

A: We have to find the closed sets.

Q: Part II. Calculating Second Order Partial Derivatives. Find all the second order partial derivatives…

A: Note : As per our guidelines we are supposed to answer only 3 subparts if there are multiple subpart…

Q: Find fx (x,y) and fy(x,y). Then, find fx(1, -2) and fy (-3,3). 4 f(x,y) = -2xy +9y² + 10 fx(x,y)=

A:

Q: 3. Emily is making a closed rectangular box with a square base from two different woods. The wood…

A: Use minimizing concept

Q: Your are driving away from Tulsa. Your distance (in miles) away from Tulsa x hours after 12:00 noon…

A: Given problem:- Your are driving away from Tulsa. Your distance (in miles) away from Tulsa x hours…

Q: 2. f(-7sinx + 3cosx)dx (-7sin 3. √(3x − 2 + sin x) dx TE 4. (3 sec² x + 4 csc² x) dx

A: