. Expand: (i) (2x - 3y)4

Q: An integer in (1, 2, 3,..., 25) is selected at random. Find the probability that the number is (b)…

A: We know that prime number is a whole number greater than 1 whose only factors are 1 and itself. No.…

Q: 2. Let S = {100, 101, 102,...,999} so that [S] = 900. (a) How many numbers in S have at least one…

A: We need to find number of digits.

Q: The function Ур is a particular solution to the specified nonhomogeneous equation. Find the unique…

A: To find out the solution of the differential equation.

Q: Question 1 What is a suitable IF for solving the linear equation ty' + y = cost, t> 0 OA. B. OC 3t…

A: Given, ty'+32y=cos(t), t>0

Q: Find F as a function of x and evaluate it at x = 0, x = π/3, and x = π/2. - f*cos(e F(x) = cos(8) de

A:

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use…

A: We need to find out possible error in volume and surface area.

Q: Find the critical point(s) of the function f(x, y) = x² + y² − 40xy. Enter your answer as an ordered…

A: To find the critical points of the function fx, y=x4+y4-40xy.

Q: Use the e- definition of a limit to compute the value of the following limits: 1. 2. lim 2² – 5

A: We  will find the required  limit.

Q: Define R as the region bounded by the functions f(x) = 1 and g(x) = e between x = 0 and x = 1. If R…

A:

Q: Let z(x, y) = x¹y where x = t² & y = t¹. dz dx dy & by first finding dt dt Calculate dx dt ▬▬ = dt…

A:

Q: 5. Let w = f(u, v), where u = x + y and v = x - y. Show that дw ди дх ду = () - ( ) 2

A: Given, w=f(u, v) where u=x + y and v=x - y To prove: ∂w∂x∂w∂y=∂w∂u2-∂w∂v2

Q: Let u(t) = 2t³1+ (t²-1)J-8k. Compute the derivative of the following function. (+¹2 +4t) u(t) Select…

A:

Q: A tank contains 5000 L of pure water. Brine that contains 30 g of salt per liter of water is pumped…

A:

Q: Let S be the solid inside the sphere x2+y2+(z-3)2 = 9 and the below the cone x2+y2 = z2.   Setup…

A:

Q: answer is incorrect

A:

Q: FB 2.2 Find exact expressions for the sine and cosine of 12

A:

Q: Solve y'' + y' 6y = 0, y(0) = 2, y'(0) = y(t) = 21

A: To find solution of differential equation

Q: 1. Among 200 people, 150 either swim or jog or both. If 85 swim and 60 swim and jog, how many jog?

A:

Q: Moving to another question will save this resport ion 1 Identify which of the following derivative…

A:

Q: Question Which of the following statements applies to the convergent alternating series n=1 (−1)n+1…

A:

Q: Find an equation for the tangent to the curve at the given point. Then sketch the curve and the…

A: The given function y=-2x3 at the point 1,-2 We have to find the equation of the tangent line and…

Q: Find the area of the shaded region bounded by the two axes and the curve y = 2 sin(x) + 1. f(x) 2…

A: The bounding curves of the region are: C1: y = 2sinx+1C2: y = 0C3: x = 0 The sketch of the region is…

Q: f(x) = x² - 11x + 30 g(x) = x - 5 (f+g)(x) = (f- g)(x)

A:

Q: Use logarithmic differentiation to find the derivative of the given function. = (3x² +7²)² (x−³ −…

A:

Q: 2. Find (F(r(t))) when F and r are the functions given below. (a) F(x, y) = sin(x) + cos(y) and r(t)…

A: According to our guidelines,i can solve only first please reroute the remaining question.

Q: A clothing business finds there is a linear relationship between the number of shirts,n, it can sell…

A:

Q: Solve the queation 36x cubed + 45x squared - 7x - 4 = 0 given that -4/3 is a zero of f(x)=36x cubed…

A: Please see the below picture for detailed solution.

Q: The following graph of the function f satisfies limf(x) = 2 . For = 3 find a value of 8>0 such that…

A:

Q: Suppose that for a given curve defined parametrically, dy dx dt = sint. Then dx² dy dt = tant and

A:

Q: 1. Each of the following integrals can be found by making a substitution u for part of the…

A:

Q: If 1 f(æ) = tanh-Và then f'(x) = 0

A: Given: fx=tanh-1x4 To find: f'x Required formulas:  ddxtanh-1z=11-z2 Power rule: ddxxn=nxn-1 Chain…

Q: Find the first partial derivatives for f(x,y) = 10x cos (xy). 4:0 | 빙 = 11

A:

Q: Find the equation for the horizontal asymptote of the graph of the function. 2x² - 7x-9 1-3x - 6x²…

A: We have to find horizontal asymptotes for given function.

Q: Define as the region bounded by the functions u(y) = y² + 1 and v(y) = y between y = 1 and around…

A: Graph:-

Q: Find an nth degree polynomial function with real coefficients satisifying the given conditions n=3…

A:

Q: 11. Cards are drawn from a deck of 52 cards with replace- ment. (a) In how many ways can ten cards…

A: Given that cards are drawn from a deck of 52 cards with replacement.

Q: When a quarter is tossed four times, 16 outcomes are possible. HHHH HHHT HHTH HHTT HTHH HTHT HTTH…

A:

Q: Find the critical point(s) of the function f(x, y) = x¹ +y¹ − 40xy. Enter your answer as an ordered…

A:

Q: The graph of the function f(x) = x³ is translated horizontally to create g(x). If the point (4, 8)…

A: We can solve this as follows:

Q: Evaluate the derivatives. Do not simplify. (a) ey - y² = ln x tanz (b) y = (secx)*

A:

Q: Find the rate of change of a population of size P(t) = ³ + 4r + 10 at time! = 4. The rate of change…

A: P(t)=t^3+4t+10         rate of change=dP(t)dt             dt^ndt=nt^n-1

Q: Use the quotient rule to find the derivative of -4 sin(x) - 3 3x¹0 +7 You do not need to expand out…

A: Given query is to find the derivative of the expression.

Q: Consider the following. 3x³ - 27x² + 5 y = (a) Find the critical values of the function. (Enter your…

A:

Q: Evaluate the definite integral. Your answer will be a function of a. - 8t + 5) dt =

A:

Q: Express the integrand as a sum of partial fractions and then evaluate the integral. SX² 4 x-1 dx…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Evaluate the following integrals and state that they diverge or converge.

A:

Q: Differentiate the following function 3 U = ²³² √² + ² + 2 u= +2√+³

A: Derivate with respect to t

Q: Use a Double- or Half-Angle Formula to solve the equation in the interval [0, 2). (Enter your…

A:

Q: Suppose that lim f(x)=15 and lim g(x)=-8. Find the following limits. x-b a. lim (f(x) + g(x)) b. lim…

A: Here we have to use the concept of limits

Q: 3. Rewrite 3 log2 (a) + 4 log2 (b)-5 log₂ (c) as an expression of the form log2 (something).

A: