2) If f(x) = x - 5 and g(x) = x² + 3; Find the following: [g(f(x)), g(g(x)), f(f(2)), g(g(-5))]

Q: Find the solution set of the given equations/inequalities. Check for extraneous roots/solutions. 2x…

A: Given equation, 2x-12x-3-xx+1-2x+12x2-x-3=0

Q: Let S = n=1 1 n+√n 1 2n 1 n+ √√n Verify that for n ≥ 1, 1 n+√√n M 1 √n Can either inequality be used…

A: Given:           S=∑n=1∞ 1n+n For                  n⩾1Whether the following information  1n+n⩽1n can…

Q: The mathematical models is only nonlinear equation describing the models? True False

A: There are different types of mathematical models present and among these different types , there is…

Q: Question 4. Find all solutions of each first order differential equation. dy dx (a) xy

A:

Q: Prove that the lateral surface area of a right circular cone with height h and base radius r is S =…

A:

Q: Assume a savings account had $9000 initially, and that the interest rate per year to be compounded…

A:

Q: 3. lim 0-0 sin 8 sin 20

A:

Q: Find the domain and range and draw the graph. 1. f(x) = 2x+1 , for ≤ -2 -2 ,…

A: 1) f(x) = 2x+1 , for x≤ -2     = -2 ,       for x>2 Domain of the function is x ≤ -2 and x>2…

Q: (h) The Root Test can always be used to determine whether an infinite series converges or diverges.

A: We need to comment on the following statement: The root test can always be used to determine whether…

Q: What does g(5 t + 5) do to the function g(t)? O compress horizontally by a factor of 1/5 and then…

A:

Q: 4. Which of the following is a weak, partial, linear order or equivalence relation? Why? (a) ≥ on Rn…

A: (a)   ≥ on ℝn  is a weak, partial, linear order because it is a linear order on a subset of R.   (b)…

Q: 204. A boy rides a bicycle along the Quezon Bridge at a rate of 6 m/s. 24 m directly below the…

A: This is a problem related to Pythagoras theorem and its derivative. Please follow the procedure…

Q: Find the Domain and Range for b

A:

Q: Find the derivative of the function. y = V 11x + +√ 11x + y' = X √11x

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

Q: Graphically solve the equation and inequality below. Sketch the graph(s) that you used and round…

A: To solve the given equation graphically.6x2-2x3=-x2+5x+1

Q: Find the domain and range and draw the graph. f(x) = -4 , x > 0            2 , -2 ≤ x ≤ 0…

A:

Q: For the differential equation given below, variable. d²q dq 1 L²+²+4=E +R dt d₁2 C is the…

A:

Q: Find the equation of the line with the given properties. Express the equation in general form or…

A:

Q: 4. Non-calculator: Find a nonzero value for the constant k that makes f(x) continuous at x = 0: tan…

A:

Q: Find the limit of the function (if it exists). (If an answer does not exist, enter DNE.) x²-81 lim…

A:

Q: A. Given that the 2nd term of a geometric series is -6 and the 5th term is 2014. i. Find the first…

A:

Q: The graph of f is shown on the coordinate plane. Selected values for g are shown in the table. Graph…

A: As given that limx→af(g(x))=flimx→ag(x)And also we know that limx→af(x)n=limx→af(x)n, where n is a…

Q: x + 3 2x+3 5. (a) Find f(a) for a = -2,-1,0, 1 if f(x) = x + 2 2 4-x for x 1 (b) Find lim f(x) and…

A: Given: For (a), f(-2)=2(-2)+3=-1f(-1)=DNEf(0)=0+2=2f(1)=2

Q: 2. Non-calculator: Sketch the graph of f(x) and identify any values of c for which limx→c f(x) does…

A: To sketch the graph and check at which point limit does not exist.

Q: The graph of f is shown on the coordinate plane. Selected values for g are shown in the table. Graph…

A:

Q: 5. The derivative of the function y = A. TRUE y²-8 y² +8 is equal y' B. FALSE = 48 (v³+8) ²

A:

Q: lim x →→2 2x²+x-6 x² +5-3

A:

Q: All points of plane PL are equidistance from point (2,-1,1) and (3,1,5), find equation of PL

A:

Q: Consider the following. f(x) = -x² + 1 Find the x-values at which f is not continuous. Which of the…

A: Answers are correct but both point of discontinuities are non removable.

Q: (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(3, -4).

A: Given that y=42-xSolution :equation of tangent line at x1,y1 having slope m.y-y1=mx-x1x1,y1=3,-4m=4…

Q: 2 (0² 20 0 Ans v=c₁ +c+.

A:

Q: For the function f whose graph is given, determine the following limits. a. lim f(x) x-4 d. lim f(x)…

A:

Q: obtain the half range x10<x< f6€) £² M L x L x gine Series for

A: To find- Obtain the half range sine series for  fx = x0 &lt; x &lt; π20π2 &lt; x &lt; π

Q: lim X118 7x - √√√4x6+x5 x − x² + 3x³

A:

Q: 30+ 28- 26- 24 22 20- 18- 16 14 12: 2 8 10 12 14 16 18 20 22 The per capita consumption of breakfast…

A: The consumption of breakfast cereal in U.S Ct=-0.0031t3+0.12t2-0.35t+11.5 pounds, where t is the…

Q: Find and simplify the expression if f(x)=x²-2. f(3+h)-f(3) f(3+h)-f(3) =

A: Solution: f(x) = x2 - 2

Q: Find the derivative of the function. y = In(x√x² - 9)

A: To find out the derivative.

Q: Determine whether the series converges absolutely, conditionally, or not at all.

A:

Q: Determine each integrating factor to make the Differential Equation exact then solve each equation.…

A: Here we have to solve the differential equation.

Q: M8 n=2 1 n2 – n

A:

Q: Show that (u-v) > Show that u xv||² Find the

A:

Q: Suppose that f(5) = 1, f '(5) = 5, g(5) = -3, and g'(5) = 6. Find the following values. (a) (fg)'(5)…

A: It is given that: f(5)=1, f'(5)=5, g(5)=-3, g'(5)=6 Let us assume f(x) and g(x) are functions of x.

Q: 2. Draw a sketch of the piece-wise defined function -3, x≤-1 1,-1<x<2 4,2<x g(x)= and determine its…

A:

Q: Consider the following. sin(6x) X lim X-0 Create a table of values for the function. (Round your…

A: We need to find limit.

Q: 3 6456

A: To solve the expression

Q: Oil Production in Mexico The following graph shows approximate daily oil production by a country's…

A: The graph shows daily oil production by a country's national oil company in million of barrels per…

Q: (q) f(x) = sin(sin(sin(x)))

A:

Q: 3. The equation y² = cx is general solution of: A. y' = 2y / x B. y' = 2x/y C. y'=y/2x D. y' = x/2y…

A:

Q: Evaluate in polar coordinate I-** [ 5.² (x² + y²)dydx

A:

Q: 3. Evaluate the difference quotient, limx→0 f(x+Ax)-f(x) (x+4x)=x , for f(x) = 3x² + 7x + 5.

A: