Limits & Continuity Questions and Answers

Let f(x) = - +5. #1) Evaluate f(3). f(3) = #2) Solve x for f(x) = 2. X=

Let f(x) = 3x² Find f(a+h)-f(a) a) 6a +3h b) 6a +3h² c) 3h d) 3a + 3h

Fide solution A jeep and BMW enter a highway running east-west at the same exit heading in opposite directions. The jeep entered the highway 30 minutes before the BMW did, and traveled 7 mph slower than the BMW. After 2 hours from the time the BMW entered the highway, the cars were 306.5 miles apart. Find the speed of each car, assuming they were driven on cruise control. Let\(\;x\;\)represent the speed of the jeep and\(\y\;\)represent the speed of the BMW. Give your answer as an ordered pair, (\(x, y\)). \(\) EP 1 \(y=x+7\) Wrong turn. (All worthwhile journeys have a few wrong turns, right?) Ente

Fill in each blank with the appropriate number for solving the equation. √x+5-3=X a. The solution of the equation is Type your answer here b. The extraneous solution of the equation is Type your answer here

For the following exercise, evaluate each root. Evaluate the cube root of z when z = 8cis(77)

Find a vertical line x = k that divides the area enclosed by x = √√y, x = 2, and y = 0 into two equal parts.

Vectors u = -10i + 3j and v= -7i - 9j. What is u - v?

Evaluate (1 + i)* for k = 4,8, and 12. (1 + i)¹ = (1+i)= (1 + i) ¹2 = Predict the value of (1 + i) 24. (1 + i) 24 =

Solve the equation and select the solution set. 1 18 2²3 +2²3 = 289 Oa) {-7} Ob) (-3,7) Od {7} Od (-7,3}

Solve the equation and write the solution set. If necessary, use / to enter fractions, as in 34/9 means Do not enter any spaces in the answer. 27/2=4 The solution set is N

Solve the following system of equations. x + 1y+z= 1 (1) -x+ 2y + z = 2 (2) 2x- y = -1 (3) What is the solution? Select the correct choice below and fill in any answer boxes within your choice. O A. There is one solution, (... (Type exact answers in simplified form.) …… OB. The system is dependent. OC. There is no solution.

1+4z x+3 O(67+44i) O(67 - 44i) If y= I what is the value of y when x = 4i? O(67+44i) 25 O(-67 +44i) O(67-441)

Solve the rational equation and identify the solution set. 2-1 x+6 76-6x ²-36 -1 x-6 O a) {-8,8} Ob){-2√/19,2√/19) - OcØ Od) {-6, 6} Ol{2,6} =

Let a = à b a - – 7ỉ – 4j and b = 5ỉ + 6j. Find i

A plane travels 40° east of south What is its compass heading? [?]°

Solve the equation by applying the square root property. (2x-1)² = 49 Oa) {-6,8} Ob) {-8,6} Od) {-4,3} Od (-3,4} d)

4. The graph of the first derivative f' of a function f is shown. (Assume the function is defined only for 0 ≤ x ≤9.) Just write your answers from the graph. YA y = f(x) min 0 8 a) On what interval(s) is f increasing? b) On what interval(s) is f decreasing? c) At what value(s) of x does f have a local maximum? (Enter your answers as a comma- separated list.) x = d) At what value(s) of x does f have a local minimum? (Enter your answers as a comma- separated list.) x = e) On what interval(s) is f concave upward? (Enter your ans er using interval notation.) f) On what interval(s) is f concave downward? (Enter your answer using interval notation.) g) What are the x-coordinate(s) of the inflection point of f? (Enter your answers as a comma-separated list.)x =

Find the derivative of (sinx +x)/(2+cos x) For f(x) = 4x1/3 + x4/3, determine the intervals where the function is increasing.

A plane travels 20° east of south. What is its compass heading? [?]°

An angle passes through the point (-7, -5). What is the compass heading of this angle? [?]°

Solve the equation and select the solution set. x-1 2-² +243 = 2²4738 11 I Oa) {-3, 0} Ob) 0 Oc) {-7, 2} Od) {-2,7}

Let f(w) = (15w)" Use logarithmic differentiation to determine the derivative of f. d dw -[f(w)] = Determine the slope of f at w = 1. f'(1) =

3. Sketch the graph of a function that satisfy the following conditions: f(0) = 0, f continuous and even. f'(x) = 2x if 0<x< 1, f'(x) =-1 if 1<x<3 and f'(x) =1 if x > 3

A car travels 17° south of west. What is its compass heading? [?]°

Find the magnitude of the projection of ( — 8, 3) onto the vector ( – 5, — 5)

An airplane is heading north at an airspeed of 600 km/hr, but there is a wind blowing from the northeast at 30 km/hr. The plane will end up flying course degrees off The plane's speed relative to the ground will be km/hr

Round the number to 3 significant figures. 1.4593 Step 1: Identify the digit we need to check for rounding. What is the place value for the last significant figure in the answer? A. the ones C. the hundredths B. the tenths D. the ten thousandths

Round to 3 significant figures. 6,578,304 Step 1: Identify the digit we need to check for rounding. What is the place value for the last significant figure in the answer? A. the hundreds C. the thousands B. the hundred thousands D. the ten thousands

Vector component of V and W are as follows. Find the direction of the resultant vector. V= (13.5, -21.07) W = (-0.9, -14.6) [?]°

Solve the absolute value equation. 3|2x – 6| + 7 = 22

Calculus Consider the limit: limx-0+ (cosx) ¹/² 2 a. Use a graphing calculator to find the limit. b. Find the limit analytically.

Round to 3 significant figures. 6,578,000 Step 2: Now we need to round the number up or down. What is the answer rounded to three significant figures?

Let à = (4, 3) and b = a (0, k). Find k so that a and b will be orthogonal (form a 90 degree angle). k= Enter a mathematical expression [more..]

Three different forces act on an object. They are: F₁ 1 < 2, − 3 > 2, 5 > < −8, − 5 > F₂ 2 F3 = Find the net force Fnet on the object (the sum of the forces) Fnet FA Find what fourth force, F4 would need to be added so the object feels no force, that is, so Fnet = 0 = =

Let h(t) =tan(2x + 3). Then h' (1) is and h''(1) is

Which pair of lines are parallel? a. x+7y-2=0, r = (2,5)+s(1,7), se R 3x-4y-2=0, r = (1,4) +s(-3,4), s € R c. 2x+2y+2=0, r = (1,2) + s(1,-1), se R b. e d. none of the above

At a computer store, a customer is considering 6 different computers, 9 different monitors, 7 different printers and 4 different scanners. Assuming that each of the components is compatible with one another and that one of each is to be selected, determine the number of different computer systems possible. There are different computer systems possible.

A man has 10 shirts and 3 ties. How many different shirt and tie arrangements can he wear? He can wear different shirt and tie arrangements.

A true-false test consists of 5 questions. a) In how many ways can the test be completed, selecting true or false for each question? b) What is the probability that a test is randomly answered perfectly? a) In how many ways can the test be completed, selecting true or false for each question? The test can be completed in ways. (Type a whole number.) b) What is the probability that a test is randomly answered perfectly? The probability is (Type an integer or a simplified fraction.)

The DNA molecule is a double helix consisting of two strands joined by bonds involving 4 substances called bases: adenine, cytosine, guanine, and thymine. Assume that these bases are uniformly distributed along an entire strand of a DNA molecule. A geneticist randomly selects 8 consecutive bases in a DNA molecule for study, a) How many sequences of the 8 bases are possible? b) What is the probability that the sequence consists of 2 cytosine and 6 guanine bases? c) What is the probability that the sequence does not consist of 4 adenine and 4 thymine bases? a) There are possible sequences. (Simplify your answer.) b) The probability that the sequence consists of 2 cytosine and 6 guanine bases is (Type an integer or decimal rounded to four decimal places as needed.) c) The probability that the sequence does not consist of 4 adenine and 4 thymine bases is (Type an integer or decimal rounded to four decimal places as needed.) BILB

6. The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares? The possible sum of the squares is show your work below.

Assume that certain types of identification numbers range from 00-00-000 to 77-77-777, where only the digits 0 through 7 are used. An identification number is randomly selected. a) What is the probability that the identification number contains 7 different numbers? b) What is the probability that the identification number contains at least one repeated digit? a) What is the total number of possible identification numbers? (Simplify your answer.) The probability that the identification number contains 7 different numbers is (Type an integer or decimal rounded to four decimal places as needed.) b) The probability that the identification number contains at least one repeated digit is (Type an integer or decimal rounded to four decimal places as needed.) SELLE 4

Six fair six-sided dice are rolled. An outcome is an ordered sequence of 6 numbers between 1 and 6. For example, the sequence 1-1-1-1-4-3 is different from the sequence 4-1-3-1-1-1. a) How many outcomes are possible? b) What is the probability that a roll results in 6 different numbers? c) What is the probability that a roll results in 6 of the same number? a) The number of possible outcomes is (Simplify your answer.) b) The probability that a roll results in 6 different numbers is (Type an integer or decimal rounded to four decimal places as needed.) c) The probability that a roll results in 6 of the same number is (Type an integer or decimal rounded to seven decimal places as needed.) - 4

f(x)=√4x-5 g(x) = 5x-1 Find f-g and fg. Then, give their domains using interval notation. (f - g)(x) = Domain of f - g : (f*g)(x) = Domain of f*g : C D

Find the 34th derivative of the function f(x) = cos(x). The answer is function

f(x) = √5x-3 g(x)=x²+4 Find f+g and fg. Then, give their domains using interval notation. (f + g)(x) = Domain of f + g : (f.g)(x) = Domain of fig 2

Mr. Tappis doesn't like to wear the same outfit twice in a school year (yeah, right).' At the beginning of the year, he had 5 pairs of pants, 2 pairs of shoes, and 7 shirts. If the school year is 180 days long, how many more pairs of pants does he need to buy before the school year started to not wear the same outfit twice?

Find the derivative of ƒ(x) = −4√x – 6 - X4 Type your answer without fractional or negative exponents. Use sqrt(x) for √x. f'(x) = ( C vi

Find the limit. (If the limit is infinite, enter 'oo' or '-00', as appropriate. If the limit does not otherwise exist, enter DNE.) x-8x²+x x-x³-x+6 lim

Find the following limit: 2x² lim I→7 x³ Answer: - - 38x + 21 x - 7