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# Calculus

## Calculus

 1 Verify the identity.     cot θ ∙ sec θ = csc θ 2 A gas company has the following rate schedule for natural gas usage in single-family residences:     Monthly service charge                  \$8.80   Per therm service charge 1st 25 therms                      \$0.6686/therm Over 25 therms                  \$0.85870/therm   What is the charge for using 25 therms in one month? What is the charge for using 45 therms in one month? Construct a function that gives the monthly charge C for x therms of gas. 3 The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is     W(t) =     where v represents the wind speed (in meters per second) and t represents the air temperature . Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second. (Round the answer to one decimal place.) 4 Complete the following:   (a)           Use the Leading Coefficient Test to determine the graph’s end behavior. (b)           Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. (c)           Find the y-intercept. f(x) = x2(x + 2) (a).         (b).         (c). 5 For the data set shown by the table,    a. Create a scatter plot for the data. (You do not need to submit the scatter plot)  b. Use the scatter plot to determine whether an exponential function or a logarithmic function is the best choice for modeling the data. Number of Homes Built in a Town by Year 6 Verify the identity.   (1 + tan2u)(1 – sin2u) = 1 7 Verify the identity.   cot2x + csc2x = 2csc2x – 1 8 Verify the identity.   1 + sec2xsin2x = sec2x 9 Verify the identity.   cos(α – β) – cos(α + β) = 2 sin α sin β 10 The following data represents the normal monthly precipitation for a certain city.   Draw a scatter diagram of the data for one period. (You do not need to submit the scatter diagram). Find the sinusoidal function of the form  that fits the data.
Multiple Choice: Type your answer choice in the blank next to each question.

_____11. The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the graph to answer the question.

Does the graph represent a function?

 A. Yes B. No

_____12. Find the vertical asymptotes, if any, of the graph of the rational function.

f(x) =

 A. x = 0 and x = 4 B. x = 0 C. x = 4 D. no vertical asymptote

_____13. The formula A = 118e0.024t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 140 thousand?

 A. 2008 B. 2005 C. 2006 D. 2007

_____14. Find the specified vector or scalar.

u = -4i + 1j and v = 4i + 1j; Find .

 A. B. 8 C. 2 D. 5

_____15. Find the exact value of the trigonometric function. Do not use a calculator.

 A. -1 B. C. 1 D.

_____16. Find the x-intercepts (if any) for the graph of the quadratic function.

6x2 + 12x + 5 = 0

 A. B. C. D.

_____17. Use the compound interest formulas A = Pert and A = P to solve.

Suppose that you have \$11,000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually?

 A. \$11,000 invested at 6.25% compounded continuously over 10 years yields the greater return. B. Both investment plans yield the same return. C. \$11,000 invested at 6.3% compounded semiannually over 10 years yields the greater return.

_____18. Find functions f and g so that h(x) = (f ∘ g)(x).

h(x) = (6x – 14)8

 A. f(x) = 6x – 14, g(x) = x8 B. f(x) = 6x8 – 14, g(x) = -14 C. f(x) = x8, g(x) = 6x – 14 D. f(x) = (6x)8, g(x) = -14

_____19. Begin by graphing the standard absolute value function f(x) = | x |. Then use transformations of this graph to graph the given function.

h(x) = 2 | x | + 2

 A. B. C. D.

_____20. Find the reference angle for the given angle.

-404°

 A. 44° B. 46° C. 134° D. 136°

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Author Since: December 1, 2020