M1

h(x) = f(g(x)), f(x)= 1/x-3, g(x)= x^2 +5

(-infinty dign, infinty sign) x= DNE There are no discontinuities; f(x) is continuous.

THIS TWO HAVE THR SAME ANSWER Consider the following. f(x) = 2 − 7x − x^2 & f(x) = 9/x^2 + 6 & f(x) = 8 - 3x -x^2 Describe the interval(s) on which the function is continuous. (Enter your answer using interval notation.) Identify any discontinuities. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) If the function has any discontinuities, identify the conditions of continuity that are not satisfied. (Select all that apply. Select each choice if it is met for any of the discontinuities.)

(-infinty sign, infinty sign) X = DNE There are no discontinuities; f(x) is continuous.

x ≤ - 1 x > -1

(-infinty sign, infinty sign) x= DNE There are no discontinuities; f(x) is continuous.

Find the derivative of the function. y = 7x^3 − x^2 + 6x − 7

21x^2 - 2x + 6

y= 6x/x^-3

24x^3 Step 1: multiple the top number by the with postive version of the bottom number plus. Step 2: the negative power number will become postive.

f(x)=14x^1/7

2x^-6/7 Step 1: divide the bottom of the fraction by the main number. Step 2: The power will be -6/7.

find the limit lim x→ -1 5x^2 - x - 6/x + 1

=5x-6 5(-1) - 6= -11

lim x→9 (-x^2 + x -9)

CAUTION: THIS SHOULD BE A NEGTIVE NUMBER. = -81

lim x→13 √x + 3 − 4/x − 13

CAUTION: THIS WILL BE A FRACTION Step 1: The top part will be 1 Step 2: √x+3 +4 = 1/8

f(x)= 1/x^2 - 9 THIS WILL HAVE A GRAPH WITH BLUE-DOTTED LINE

Describe the interval(s) on which the function is continuous. (Enter your answer using interval notation.) (- infinty sign, -3)U(-3,3)(3,infinty sign) Identify any discontinuities. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) (-3,3) If the function has any discontinuities, identify the conditions of continuity that are not satisfied. (Select all that apply. Select each choice if it is met for any of the discontinuities.) There is a discontinuity at x = c where f(c) is not defined. There is a discontinuity at x = c where lim f(x) x→c does not exist.

f(x) = x^3 + x + 6, (-2,-4)

Find an equation of the tangent line to the graph of the function at the given point y= 13x + 22 Graph Answer: Going towards the right. It's close to zero.

f(x)= (2x + 1)^2 (0,1)

Find an equation of the tangent line to the graph of the function at the given point. y=4x +1 Graph: The Dip is on the left and it's the closet to zero.

This question will have graph answers with two lines on with open dot and another closed. x ≤ 0 x > 0

Graph Answer: Both of the lines go up. black is left and white is right (-infinty signs, 0) , (0, infinty sign) removable discontinuities x=DNE nonremovable discontinuities x=0

Consider the following. - 1 ≤ x ≤ 1 1 < x ≤ 4

IMPORANT: USE THE SQUARE parenthesis It is the first number from the first row. The last number of the second row. -1,4 x=DNE There are no discontinuities; f(x) is continuous.

y= x^2/ x^2 - 16 This graph will look like a black dotted road and with 3 a red curve lines.

It will be the square root of bottom number with +-. The function is differentiable for all x ≠ ±4. The function is not defined at those values.

Consider the following. f(x)= x - 8/x^2 - 64 Describe the interval(s) on which the function is continuous. (Enter your answer using interval notation.) Identify any discontinuities. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) If the function has any discontinuities, identify the conditions of continuity that are not satisfied. (Select all that apply. Select each choice if it is met for any of the discontinuities.)

MAYBE: I think the reason this is different than other is becuase the top bit is the square root of the bottom. (-infinty sign, -8)U ( -8,8)U(8,infinty sign) x= -8,8 There is a discontinuity at x = c where f(c) is not defined. There is a discontinuity at x = c where lim x→c f(x) ≠ f(c). There is a discontinuity at x = c where lim x→c f(x) does not exist.

The population P (in thousands) of a country can be modeled by P = −14.75t^2 + 788.5t + 117,218

Part A: simply plu g and chug THE POPULATION IS GROWING Part B: I will need to modifty the function. -29.5t+788.5 Then plug and chug. The rate of growth is decreasing.

A = 9,000(1 + r/4)^80 You deposit $9,000 in an account that is compounded quarterly at an annual rate of r (in decimal form). The balance A after 20 years is given below. What is the limit of A as the interest rate approaches 6%? (Round your answer to two decimal places. If an answer does not exist, enter DNE.)

STEP 1: 1+r/4 STEP 2: click x^y and type 80 then enter Step 3: 9000(3.290662787) Step 4: 29615.97

f(x)=(x^2 + 9x)(x+4)

Step 1: Put them together using FOIL x^2 + 4x^2 + 9x^2 + 36x Step 2: find the derivative of the function 3x^2 + 26x +36

lim f(x) x→c = 6/5 lim g(x) x→c = 4/5 lim f(x)/g(x) x→c

Step 1: divide fractions Step 2: If the bottom of the fractions are the same, then will cancel each other out. Step 3: divide remaing numbers. 6/4=1.5

Determine whether the function is continuous on the entire real number line. Explain your reasoning. f(x)= 5/9-x^2

Step 1: square root of function is not continuous, because the rational function is not defined at ±3.

The height s (in feet) at time t (in seconds) of a silver dollar dropped from the top of a building is given by s = −16t^2 + 535. (a) Find the average velocity on the interval [4, 5]

Step 1: start with part b. Part B: Multi -16*2, then multi the velocties by -32. Step 2: go back to step 1 Step 3: Divide the last number from the first in the formula. 535/16. Then find the square root. 5.78 Step 4: multi -32*5.78=-158

y = |x2 − 9| This question will have graph that's a weird red hump "W".

The anwer will be the square root with +-. The function is differentiable for all x ≠ ±3. The graph has a cusp.

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The graph will start above 0.2. The first line is completely black. The rest of the lines start white then turn black. x=1,2,3

f(x) = x^3, x ≤ 6 ax^2, x > 6

This will always be the number on the right on the signs. 6

Determine the point(s) y=x^4 - 2x^2 + 5

This will have smallest x-value and largest x-value To find y-vaules subract 1. (x,y)= (-1,4) Smallest (x,y)= (0,5) (x,y)= (1,4) largest

lim x→2 8/x-2

WARNING: ALWAYS "DNE"

s ≤ and >

WARNING: ALWAYS DNE

C = 200(6 + 4√x)

WARNING: THIS WILL BE A FRACTION. Step 1: divide the number closest to the square symbol by 2. Then multi this ny the number outside the parenthesis. Step 2: put the product on the top of the fraction, then put √x on the bottom.

Estimate the slope of the graph at the point (x, y). (Each square on the grid is 1 unit by 1 unit.)

WARNING: THIS WILL BE NEGATIVE Start from dot, then count till it perfectly meets a square.

The graph shows the estimated number of milligrams of a pain medication M in the bloodstream t hours after a 1000-milligram dose of the drug has been given. IMPORANT: The graph will be titled PAIN MEDICATION IN BLOODSTREAM

WARNING: part a varies in answers but part b is the same. Estimate the average rate of change of M, in milligrams per hour, over the OPTION 1: .[1, 3] 275 mg per hour OPTION 2: [3, 5] -100 mg per hour Over what interval is the average rate of change approximately equal to the rate of change at t = 3.75? [2.25, 5]

P = −0.5x3 + 40x2 − 164.45x − 3000

dP/dx=−1.5x^2 + 80x − 164.45

R = 39x − x^2

dR/dx = 39-2x

g(x) = x^3 -1 Find its average rate of change over the interval [−2, 2].

Δy/Δx =4 If the numbers are the same, add them as if they're both postive. Compare this rate with the instantaneous rates of change at the endpoints of the interval. g(-2)=12 g(2)=12 Multi 4* by 3 the power. Since they intervals are both two it's the same.

Consider the following function. f(x)= -x^2 - 10x - 4 Find its average rate of change over the interval [−5, 1]

Δy/Δx=-6 Subscrat 1 from -5 Compare this rate with the instantaneous rates of change at the endpoints of the interval. f(-5)= 0 This will always be ZERO if the numbers aren't the same. f(1)= -12 -6 *2 the power