From a group of 18 student representatives, 5 will be chosen to work on a fundraising committee. How many committees are possible?

Q: Find the directional derivative of the function f(x, y) = ln(x³ + y³) at the point (3, − 2) in the…

A: Use the gradient of function for finding the directional derivative.

Q: Find the area of the region enclosed by the following functions. a) x=y²-3 and x=y+1. (-1,-2) 1…

A: Consider

Q: 8 8 Suppose ff(x) dx = • ƒ ƒ(a) dz − −1 and 19 (2) da − −4 -1 g dx = -4. 5 5 8 Evaluate f(-2 f(x) +…

A:

Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say…

A: Given :∑k=1∞k!k6

Q: Q5: prove 1) e2-j3n-e² = 2) |e²| = ex

A:

Q: Separable DE) y'ln² y + y√√x=0 y(0) = e

A:

Q: Determine whether or not the following functions are continuous at (0,0). -1 for (x, y) = (0,0) a)…

A:

Q: 4. Evaluate the integrals below. relevant triangle in your work. | | (1 (1 + tan²0)² de (b) 1…

A:

Q: mswer below: f(x) = f(x) = (x) = -2 68 5 4 3 2 10 1 0 1 -2 -3 -4 -5 6 -7 2 -00 4 6

A:

Q: sin 4x Does it exist? '. 1. Calculate lim 2. Find lim x-2 x-2 x-2 3. Find the asymptotes of - and…

A:

Q: f(x) = (1 + ln x) ³ 3

A:

Q: Q.2 Find the derivative at each critical point and determine the local extreme value. (a) y=x√√4x² 1…

A:

Q: The equation (x-y)dx + ydy = 0 is homogeneous

A:

Q: fidencos 3 Evaluate If (n²7y) dv kabrood if G. As the solid bounded by is the parabolic cylinder…

A:

Q: @ evaluate the indefinite integral fxº ex* dx

A: Given problem:- ∫ x8 ex^9 dx

Q: x-1=2x y=2= λy Z=-λz x² + y²z² = 0

A:

Q: 3 3 3 5 2 1 , B = 21 19 1 1 (A - 5B) X = C. Given the matrices A MATC the matrix X in the equation…

A: See the answer below

Q: attached

A: We will solve the problem.

Q: Use Lagrange multipliers z = f(x, y) = x² - xy + y² to find the absolute maximum and minimum values…

A:

Q: Write a triple integral, including limits of integration, that gives the volume between z+y+z=2 and…

A: Solution

Q: Question: 4 Find the value of "k" such that the function f(x)=x² + kx-6 satisfies the hypothesis of…

A:

Q: The height of each rectangle is given by the value of the function, f(x) = 5x − x2, at the…

A: Explained below

Q: Find given that cot (3x-2y)=2x-3y. dy da

A:

Q: Solve for y + In lyl at x=6: y'=(yx^2 - y)/(y+1); y(3) = -1 4.5

A:

Q: Approximate the area under the curve over the specified interval by using the indicated number of…

A: f(x) = 25 − x2 from x = 1 to x = 5; n=4 subintervals

Q: Question 11 Evaluate the limit: lim h→0 Question Help: Video (-5+h)² - 25 h

A: We can solve this as follows:

Q: You are given a piece of sheet metal that is twice as long as it is wide and has an area of 800 m².…

A: Concept: Maxima and minima: The highest and smallest values of a function are its extrema. Maxima…

Q: Evaluate the given Laplace transform xe { filt L (t-T)²cos(2T)dt

A:

Q: x² - 4x-5 x-5 x² +6x + 8 x+2 13. What is the limx-5 14. What is the limx→-2 15. What is the limx-…

A:

Q: 1 √√1-y² Q2: Evaluate fo y²(x² + y²)dx dy

A:

Q: Which of the following is equivalent to 7% = a + 3? log(a+3) 7 = y log7 y = a +3 log, 7 = a +3 Ology…

A:

Q: A vector with magnitude 7 points in a direction 295 degrees counterclockwise from the positive x…

A:

Q: 1. The function shown A. is continuous at x = 2 B. has a limit that exists at x = 2 C. is…

A:

Q: Find the indicated derivative. df If f(x) = x3, find dx 8 df dx |x = -11 || X 32 X = 10 X 1 2 11

A:

Q: The interest on an account increases exponentially. If an initial investment of $1000 earns $120 in…

A: Rate of increase

Q: Question 17 D, (cos(sin x)) = O-sin(cos z) - sin + cos z COS I - sin(sin z) O sin(sin x)

A:

Q: Solve for y at x=2: (4x^3-6yx^2 + 2xy^2)dx + (2yx^2 - 2x^3)dy = 0; y(1)=4

A: This question can be solved using the concept of differential equation.

Q: Which of the following relations is not a function? a.{(3,3),(2,3),(0,4),(1,4)} b.…

A:

Q: Determine where the function f(x) is continuous. f(x)=√x² - 25 The function is continuous on the…

A: We always check continuity of function in its domain . Hence the given function is continuous on its…

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as improper…

A:

Q: 3. (a) Use the Binomial Theorem to expand and simplify (3a²-4b)6

A:

Q: Determine whether the series converges. Σk³ e-k4 k=1 The series >

A:

Q: 닭 -2 3 2 2 3 -4- Y -1 3

A: Given graph of function         y= f(x)

Q: Find the area between f(x)=x²-12 and the x-axis from x = 0 and x = 3. The area is square units.

A:

Q: Find an equation for the plane through P(1,4, 4) that contains the line of intersection of the…

A:

Q: Suppose that f(x, y) = x² − xy + y² − 5x + 5y with x² + y² ≤ 25. 1. Absolute minimum of f(x, y) is…

A:

Q: Determine the maximum and minimum values of the function f(x)=cos³x on the interval x10,2x). Max…

A:

Q: Obtain the orthogonal trajectories of y=Cx^2 and compute for the positive value of y of the…

A:

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate…

A:

Q: Refer to the graph of y = f(x) = x² + x shown. a) Find the slope of the secant line joining (-4,…

A: