1. (a) lim x Find the limit. Use l'Hospital's Rule where appropriate. 3 x + 8 2 x + 2

Q: 3. Find the derivative y' for each of the following curves/functions. Show all work toward your 12…

A:

Q: Two poles are connected by a wire that is also connected to the ground between the poles. The first…

A: let Distance between first pole and acnhor point = x  distance between other pole = 5 - x

Q: Use the root test to determine whether the series 2n 4n + 9 converges or diverges. 9n + 2 n=1 Since…

A: Root test : Suppose that we have series ∑ an .Define,                 L = limn→∞ ann = limn→∞ an1n.…

Q: 8 lim x-2+ x²-4 x→2+ X x-21

A:

Q: 3) f(x, y, z)=x² + y² -2=²+ = ln(x). (1,1,1) -1/2 4) ƒ(x, y, z)=(x² + y² + =²)¯¹¹² +ln(xyz),…

A: 3)    fx,y,z=x2+y2-2z2+zlnx We have,       grad∅=∇f=i∂f∂x+j∂f∂y+k∂f∂z ∂f∂x=2x+zx ∂f∂y=2y…

Q: 3 Determine the 3rd derivative of the function f(x) = 2√√x-x³

A:

Q: 9x Area bounded by the curves y=e*, y=e³x, x=0 and x = ln2

A:

Q: 21 23 (24) EMPR Solve the differential equation by using method of un determined. coefferent;…

A:

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A:

Q: Use AXYZ, as needed, to complete the given parts. Part 1: Z 15 cm Part 2: Part 3: Part 4: Y 7 cm X h…

A:

Q: XZ 3) cos(x)-x²y + e + yz = 4, P (0,1,2)

A:

Q: Match each graph with its equation. 1 a. = |2| 1 -√7

A: To match graph of given equations. y=xy=x3y=xy=1x2y=x2y=xy=1xy=x3

Q: The table shows a proportional relationship between the number of tickets purchase and the cost.…

A:

Q: Find T(t) and N(t) at the given point. T() = N K2 r(t) = 9 cos(t)i +9 sin(t)j + tk; t= 2 =

A:

Q: du (u² + a²)² √

A:

Q: Find the differential dy of the function y Provide your answer below: dy= dx = 5x4 + 4 4x + 3

A: y=5x4+44x+3Differentiate w.r.t xdydx=4x+320x3-5x4+444x+32

Q: b) fex-c - cos x + 1dx

A:

Q: Q2: find dw/dt at given value point for the following function 1 1) w = x² + y², x = cos(t), y =…

A:

Q: Find the exact location of all the relative and absolute extrema of the function. (Order your…

A:

Q: Using trigonometric substitution, Find the new limits of integration. (A) None of the choices B 2 6…

A:

Q: Use the First Derivative Test to find the location of all local extrema for the function given…

A:

Q: [CLO-2] f(x) and g(x) are functions that are continuous on the interval -3 ≤x≤2 and satisfy 1 1…

A:

Q: Suppose f, g have the following values: f(3) = e5 and g(3) = 2. ƒ'(3) 10 and g' (3) = = 8. 4 Let y¹…

A: To find the value of y' at (3,-3).

Q: The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving…

A:

Q: Evaluate the integral improper integral (A) 1/9 B) 1/6 1/8 (D) 1/4 0 00 dx (2x-1)³

A:

Q: If U, V,w are three vectors such that each is inclined at an angle of with the other two, and that…

A:

Q: The area of a triangle with sides of lengths a and b 1 and contained angle is A = a b sin 0. If a=2…

A: Use the application of derivative to find the rate of change.

Q: Find a power series solution of the differential equation y' = 4y

A: We have to find power series solution .

Q: Find the curvature of the curve. r(t) =<2t, - 3sin t, 3cost)

A:

Q: The base of a three-dimensional figure is bound by the line y = -x + 1 on the interval [-3, 0].…

A: Solve the following

Q: Find f''(x). 5 f(x) = (x² + 5) *

A: The given function,  f(x)=x2+55

Q: Determine whether the integral is improper L' (x-4)-¹dx (A) Not improper (B) Improper

A: We can solve this as follows:

Q: Consider the equation (a-y-2)dx + (x + y - 4)dy = 0. (a) Make a transform to reduce the equation to…

A:

Q: QUESTION 12 dz State the multi-variable chain rule for if ди z=z(t. s, w), t=t(u, v), s=s(u, v), w=w…

A:

Q: Caitlyn wants to enclose a rectangular field with two internal partitions as shown. If the area of…

A: Given problem:- Caitlyn wants to enclose a rectangular field with two internal partitions as shown.…

Q: 000 000 000 000 OSE

A:

Q: 2. Boyle's law for the expansion of gas is PV = C, where P is the pounds per square inch of…

A: P V =Cdifferentiating w.r.t. time t;P dVdt+VdPdt=0P=5000 pounds per square foot.V=8 ft3dVdt=4…

Q: Question 7 Find the area enclosed by the curves y=2x², y=2√x,x= — and x = 1 A 45/51 B) 59/76 49/96…

A:

Q: Write the equation of a sine or cosine function to describe the graph. MA

A: This is a problem related to graph of the trigonometric function. Based on the general formula of…

Q: 3t AT(1) The temperature T of a person during an illness is given by T(t) = +98.6, where T is the…

A: T(t)=3tt2+3+98.6A)T'(t)=(t2+3)ddt(3t)-3t…

Q: Find two positive numbers that satisfy the given requirements. The sum of the first number squared…

A: We have to calculate first and second number

Q: Determine whether each of the following integrals is proper, improper and convergent, or improper…

A:

Q: 3. y = (x+b)(x-a). (x-b) ; y

A: A detailed solution is given below. Use logarithmic differential to solve it.

Q: 9x²-6 2x²-x²-8x+4 B D + x + 2 mx + n None of the choices 4 To evaluate A x-2 A 9 B 3 E 2 S + -dx…

A:

Q: x²-3x - 7 2 (x² + x + 2)(2x - 1) dx

A: Simplifying the given integrand: x2-3x-7(x2+x+2)(2x-1)=x2-3x-72(x2+x+2)x-12

Q: L=

A: Follow the procedure given below.

Q: 4. Compute each of the following definite or indefinite integrals. Show all work toward your answer.…

A:

Q: 5. What is the derivative of the given function below? * x² + y² = xy dy dy dx dx Option, dy dx = =…

A:

Q: Find the​ producers' surplus at a price level of p=​$70 for the​ price-supply equation below.…

A: Given problem:- Find the​ producers' surplus at a price level of p=​$70 for the​ price-supply…

Q: N) dy x dx X (1+y) y (1-x)

A: