
Concept explainers
In Exercises 9-38, identify a pattern in each list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.)

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Chapter 1 Solutions
Thinking Mathematically (6th Edition)
- In 2019 LinkedIns total revenue was 28.3% more than it was in 2018. The total revenue for the two years was 12.1 billion. Find the revenue for 2019.arrow_forwardwhats an example of hypothesis testing in real life.arrow_forwardIn many ways, hypothesis testing can be compared to a trial in court. What is the equivalent of p-value?arrow_forward
- Find the remainder in the Taylor series centered at the point a for the following function. Then show that lim |Rn(x)=0 f(x)=ex f(x) = e a=0 n-∞ First find a formula for f (n) (x). f(n) (x) = (Type an exact answer.) Next, write the formula for the remainder. n+1 Rn(x) = (n+1)! for some value c between x and 0 = 0 for all x in the interval of convergence. (Type exact answers.) Find a bound for Rn(x) that does not depend on c, and thus holds for all n. Choose the correct answer below. ex elx OC. R(x)(n+1 OE. Rn(x)(n+1) | Rn (x)| = (n+1)* = 0 for all x in the interval of convergence by taking the limit of the bound from above and using limit rules. Choose the correct reasoning below. Show that lim R,(x)=0 OA. Use the fact that lim U = 0 for all x to obtain lim |R,(x)| = el*1.0=0. OB. Use the fact that lim = 0 for all x to obtain lim |R,(x)=1+0=0. OC. Use the fact that lim A(+1) (n+1)! = 0 for all x to obtain lim R₁(x) =+0=0. e OD. Use the fact that lim = 0 for all x to obtain fim R₁(x)| =…arrow_forwardConsider the following parametric equations, x=-4t, y=-7t+ 13; -10 sts 10. Complete parts (a) through (d) below. a. Make a brief table of values of t, x, and y t x(t) y(t) 10 -6 0 6 10 (Type integers or decimals.) ○ A. b. Plot the (x, y) pairs in the table and the complete parametric curve, indicating the positive orientation (the direction of increasing t). 130 G c. Eliminate the parameter to obtain an equation in x and y. d. Describe the curve. OA. A line segment falls from left to right as t increases OB. A line segment falls from right to left as t increases OC. A line segment rises from right to left as t increases OD. A line segment rises from left to right as t increasesarrow_forwardLet R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the y-axis. -1 y=10 (1+10x) 1 y= 0, x = 0, and x=2 Set up the integral that gives the volume of the solid using the shell method. Use increasing limits of integration. Select the correct choice and fill in the answer boxes to complete your choice. (Type exact answers.) OA. S dx O B. dy The volume is (Type an exact answer.)arrow_forward
- Find the slope of the line tangent to the following polar curve at the given point. r = 1 - sin 0; Find the slope of the line tangent to the polar curve at the given point. Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. The slope of the line tangent to the polar curve at the point OB. The slope of the line tangent to the polar curve at the point (2) 1 元 (1) 6 is (Type an exact answer.) is undefined.arrow_forwardDetermine whether the following series converges. 4(-1)k Σ k=0 3k+6 Let a > 0 represent the magnitude of the terms of the given series. Select the correct choice below and fill in the answer box(es) to complete your choice. OA. The series diverges because ak is nonincreasing in magnitude for k greater than some index N and lim ak koo B. The series converges because ak is nondecreasing in magnitude for k greater than some index N. OC. The series converges because ak OD. The series diverges because a₁ = OE. The series converges because ak ak and for any index N. there are some values of k > N for which ak+1 ≥ak and some values of k > N for which ak+1 ≤ak- is nondecreasing in magnitude for k greater than some index N is nonincreasing in magnitude for k greater than some index N and lim ak K-00 OF. The series diverges because a₁ = and for any index N, there are some values of k > N for which ak+12 ak and some values of k > N for which ak+1 sak-arrow_forward1 × 1016 1 × 1041 = 1 × 10? = ? = product's exponent Part 2 (0.5 point) 1 × 1023 × 1 × 1021 × 1 × 1020 1 × 1015 × 1 × 1021 = 1 × 10? = ? = = product's exponentarrow_forward
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