Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.) In √x²(x + 2)

Q: Find all solutions to the equation. 4 cos 0 = -sin²0+4 Write your answer in radians in terms of ,…

A: cos2 θ +sin2 θ =1 Cosine function takes value in between -1 and 1.

Q: b Prove that: f(x) dx = F(x) =F(b)-F(a)

A:

Q: As you will show, exponential growth functions ekx always dominate power functions x", and power…

A: Given problem:-

Q: Check the function y=x²+1 whether have a symmetry about x or y axis

A:

Q: Let R be a plane region with area A whose boundary is a piecewise smooth, simple, closed curve C.…

A: Let's find.

Q: The graph of f(a) shifted right 3 units and shifted down 5 units. Of(r). 3-5 Of(x)= -3+5…

A: Let's find.

Q: Find c> 0 such that the area of the region enclosed by the parabolas y = x² − c² and y = c² – x² is…

A:

Q: 14. 2x²y-x³y' = y³

A: 2x2y-x3y' =y3

Q: r(t) = 8 cos(t)i +8 sin(t)j + tk; t = 2 8 √65 65 √65 0. = X 65 = 0 - 10 .

A:

Q: Solve the differential equation: (D³ + D)²y = 0

A: D3+D2y=0

Q: 32-37 FOURIER INTEGRALS AND TRANSFORMS Sketch the given function and represent it as indicated. If…

A:

Q: 1. The volume V of a right circular cone of radius r and height h is given by V = r²h. (a) Find a…

A: The derivative of f at x=a is            f'(a) = limh→0 f(a+h)-f(a)hthe instantanrous rate of change…

Q: 1. Use operator / elimination method to solve the given system dx dy + 2x + 2y+ 1 dt dt dx dy +2: dt…

A: Elimination method : In the elimination method, by using fundamental arithmetic procedures, we can…

Q: Let f(x)=(x-3)-2. Find all values of c in (2, 5) such that f(5) f(2)= f'(c)(5-2). (Enter your…

A:

Q: 64 Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

A:

Q: The plot below represents the function f(x) 9 on 7 10 M 6 a 3- 7 2- 1 -3-4-3 -1 Evaluate f(4) f(4)-…

A:

Q: Determine whether the following Consistent or not a) 5x +2y = 1 3x +2y = 1 b) X₁ + X₂-2X3 + X4 = 9…

A: Here, to check whether the given system is consistent or not.

Q: r(t) = (t, In(t), √t), to = 1 e the equations for the line to approximate r(to + 0.1). to + 0.1) =

A:

Q: The amount of trash, in tons per year, produced by a town has been growing linearly, and is…

A: Solution: Given the amount of trash in tons per year is given by P(t)=52+2t

Q: Find the equation of the tangent line to the graph of f(x) = 9 sin(x) + 4 cos(x) at x = in in the…

A:

Q: The graph of g consists of two straight lines and a semicircle as shown in the figure. y -20 y =…

A:

Q: 2 QX = X² x + 2

A:

Q: 4. Given that '(t) = (6t², 2t + 4) and that (2) = (2, 8), find r(t), where we are assuming that the…

A: We have to find the r(t)

Q: 8 765 4 3 2 1 -7-6-5-4-3-2 4 -2- -3 Clear All Draw: 4 -3 -6- 1 2 3 4 5 6 7 8

A:

Q: 2) Find the relative maximum or minimum value of f(x, y) = 3x² + 2xy + 10y² - 54x - 308y

A:

Q: Consider the following function. f(x) = 4x2/3 Find f(-8) and f(8). f(-8) = f(8) = Find all values c…

A: Here, the given function is: f(x)=4-x23

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A:

Q: = [₁²2² I = x² dx I = fa da x

A:

Q: Find r'(t), r"(t), r'(t) ・r(t), and r(t) × r"(t). r(t) = 2t2i - 2tj + 2 13배 (a) r'(t) (b) r"(t) (c)…

A:

Q: 1. Let Evaluate the following limit. 7 (t) = (t² + 5, t²-5t+6 t²-9 lim r(t). t-3 > sin(πt)).

A:

Q: 3 Consider the linear system system x +2y = 10 3x + = 30 i) Determine >lat value of t, so that the…

A: Given a system of equations.

Q: Write the first four terms of the sequence whose general term is given below. (-1)^ 4 +1

A:

Q: Evaluating a Definite Integral In Exercises 67-74 evaluate the definite integral. Use a graphing…

A: We want to evaluate the integral.

Q: Use the fundamental identities to fully simplify the expression. cot(x) cos(x) + csc(x) sin²(x) In…

A: Please see the answer below.

Q: A company has fixed costs of $5,000. Producing 300 items incurrs a total cost of $26,000. (a) Find…

A: Use derivative and average formula for cost ,for evaluating it.

Q: Evaluate the limits of the following. State the theorem(s) used. x²³ +8 lim x+2 x+2

A: We can solve this as follows:

Q: Find P(33 < X < 47) if X is normally distributed with mean 37 and standard deviation 10. For all

A:

Q: Find the arc length L of the graph of r(t). r(t) = t3 i+t L= i j+126t2 k, 3≤t≤6

A:

Q: the vector-valued function.

A:

Q: I need all the integrals of the trigonometric ratios

A: ∫sin x=-cos x+C∫cos x=sin x+C∫tan x =-ln|cosx|+C

Q: Select all of the following graphs which represent y as a function of z. 3 20

A:

Q: A vector u has an initial point (1,2,3) and terminal point (6,9,1). Find a vector v that has the…

A:

Q: Determine whether the series is convergent or divergent. If the series is convergent determine the…

A: Given problem:-

Q: . [0/1 Points] DETAILS PREVIOUS ANSWERS OSCA Use the fundamental identities to fully simplify the…

A:

Q: Q2):- Find Y[Z] of signal Y[n] (Cos wn). U[n]

A:

Q: Consider the following function. 13 f(x) = - In x 13 (a) Find the critical numbers of f. (Enter your…

A:

Q: Intervals on Which a Function Is Increasing or Decreasing In Exercises 21-28, find the open…

A: h(x) =x+21/3+8  Or, h'(x) =13x+2-23   We know that,  i) If f'(x) &gt;0 for every x on the interval I…

Q: MY NOTE An open box of maximum volume is to be made from a square piece of material, s = 30 inches…

A: Given: S= 30 inches

Q: Let G₁ be z = 6-√√36 - x² - y² and G2 be the upper nape of x² + y² - 3z² = 0. If S is the circle…

A:

Q: When records were first kept (t = 0), the population of a rural town was 230 people. During the…

A: Population model