2b. Explain the difference between a partial derivative and a directional derivative.

Q: In 2 Use the formula t= that gives the time for a population, with a growth rate k, to double, to…

A: We need to find growth rate and time to double the population.

Q: Fourier Series Exercise 1. Consider the following periodic function f(t) of period of 27 over the…

A:

Q: 1. f (5x¹8x³ 2. f (4x + 2) de +6x² - 4x + 7) dx

A: Topic:- integration

Q: Farmer Jones, and his wife, Dr. Jones, decide to build a fence in their field, to keep the sheep…

A:

Q: 1 0 0 1 -1 1 -1 1 1 1 0 a) Find A-¹. b) Write the corresponding elementary matrix for each row…

A: We will solve the given question using the inverse matrix method To find the inverse of matrix A…

Q: x = 48 cos(t),

A: answer is in next step

Q: Evaluate lim X→∞ ९+2 1 - x³ ( if necessary, using L'Hôpital's rule)

A: limx→∞ex21-x3Apply L-Hospital rulelimx→∞2xex2-3x2limx→∞2ex2-3x

Q: Using integration by parts, Then k is? (a) - 1.5136 ²x³ cos x³ cos(x²) dx = k - [*x sin(x²) dx 0…

A: Solve it

Q: Find F'(x). 1. F(x) = √x+² (4t + 1)dt 2. F(x) = f*t³dt SOLUTION IN HANDWRITTEN

A:

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 6 - 6…

A:

Q: Consider the following system of linear equations 4 4 -2 30 1 0 18-0 7 -2 -3 2 -18 Which one, among…

A:

Q: Q1: Find partial derivatives of the function with respect with each variable 3) f(x, y) = (xy-1)² 2…

A:

Q: Question 2 Select all of the following tables which represent y as a function of z. I y Iy I y I y…

A: Given query is to find which table is a function.

Q: √a²-x² -dx √a²-x² X --Arcsin (). + c

A:

Q: Q2: find dw/dt at given value point for the following function

A:

Q: Q3: Find gradient of the following function at given point 1) f(x,y)=y-x, (2.1) 2) g(x,y)=y-x²,…

A: As per as our guidelines i am supposed to answer only three part of this question.

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: f(x, y) = 3x² - y x4 x² + 2y ² 1 (x, y) = (0,0) 2 D (X,Y)= (0,0) 1 Determine if f is continuous at…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) / G 6.9 + +0.5 +0.5 5ex dx 6 -

A:

Q: 12. 13. 14. √2+6-√√6 Т lim I-0 LIMIT VALUE: lim 2-1 LIMIT VALUE: Т lim 3 2-8 V 11-2z LIMIT VALUE:…

A: limx→a f(x) =L if and only if limx→a+ f(x) =limx→a- f(x) .

Q: r₁(t) = cos(t)i + sin(t)j +5tk, r₂(t) = 4i + tk X d -=[r₁(t) · r₂(t)] 10 t - 9 sin(t) = dt d -[r₁(t)…

A:

Q: a cone-shaped paper drinking cup is to be made to hold 27 cm3 of water. Find the height and radius…

A:

Q: A hot air ballon is hovering 83 meters above the ground and begins to assend at a rate of 9 meters…

A:

Q: Use a sum or difference formula to find the exact value of the following. sin 148° cos 103° - cos…

A:

Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 4 1 lim t+oo 5t² + 6'8t = (?, ?)

A: Solved below.

Q: [sin³ (2) cos(4) dx

A: Follow the procedure given below.

Q: Question 10 Complete the description of the piecewise function graphed below. Enter the domains as…

A: To find for which intervals does the given values of f(x) are obtained.

Q: 7(e)₁² X y= » - [1-171² 2 sec- y = (tan 17 1² ² X y = [cscx]arcsin (cos.x)

A:

Q: Suppose f(-3) = 5, f'( − 3) = 5. f(-3.02) ~ decimal places) Approximate f( – 3.02). - (enter your…

A: I am attaching image so that you understand each and every step.

Q: A B Consider the integral f sin ¹x dx. If we let u = sin-¹x and dv= dx, the integral can be written…

A:

Q: tan6(x) cos4(x) sin²(x)sec³(x) [7sin²(x) + 9cos²(x)] + C A 63 tan²(x) [7tan²(x) +9] + C B 36 Ⓒ…

A:

Q: Use the information given below to find sin (a-³). 12 tan a = with a in quadrant III I 5 3 cos B =…

A:

Q: g(x) a b Suppose g(x) = f(x) +3 a= 2 and b=7 Compute the area between fand g using 2 and 7 as your…

A:

Q: 13. Find the mass of a thin funnel in the shape of a cone z = √x² + y²,1 ≤ z ≤ 4, if its density…

A: answer is in next step

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

A: topic - limits a3+b3=(a+b)(a2+b2-ab)

Q: 5) 5) g(x, y) = x²y + cos(y) + y sin(x) r(x, y) = ln(x + y)

A:

Q: Explain why you think the sequence 7 converges to a finite number or (-8)"-1 diverges. If the…

A:

Q: The series ∞ (-10) k k! k=1 is an alternating series but we can apply the ratio test to ∞ (-10) k k!…

A: We have to check convergence of series with the help of ratio test.

Q: Find a set of equations to represent the graph of the rectangular equation using t=x and t=2-x. y=…

A: The given rectangular equation,y=4x-2

Q: 3. Let h = f(t) be your height (in meters) above the ground while riding a Ferris wheel. The Ferris…

A: Given that the wheel complete one revolution in 8 minutes.

Q: 8 lim x-2+ x²-4 x→2+ X x-21

A:

Q: Given the integral [ cot³x csc5x dx. If u = cscx, then the integral can be re - written as: (a). f…

A: We will substitute u=cscx and then calculate the rest.

Q: Solve the optimization problem. F = Minimize F = 11x² + 11y² with xy² = 16.

A: Given problem:- Solve the optimization problem.   Minimize F = 11x2 + 11y2 with xy2 = 16

Q: i mylliplied to ma constraints. ng range, and x minimize the function of lagi zo constraigher y of…

A: Use Lagrange theorem

Q: y = (2x²+1) 3x²+1 2

A:

Q: || ti + t²j||dt|

A: Explanation of the answer is as follows

Q: 1. S-10 sin 5x dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r =…

A:

Q: A group consists of four men and seven women. Six people are selected to attend a conference a. In…

A: