Mathematics, 23.01.2020 08:31 Casmereee

Calculus question, just the first line. other stuff is just my

Answers: 3

Show answers

Answers

Answer from: litman876

$\displaystyle \int\limits^{\infty}_{\frac{\pi}{2}} {\frac{7}{x^{\frac{1}{2}}}} \, dx = \infty$

General Formulas and Concepts:

Algebra I

Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Calculus

Limits

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Limit Property [Multiplied Constant]: $\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)$

Integrals

Definite IntegralsImproper Integrals

Integration Constant C

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^{\infty}_{\frac{\pi}{2}} {\frac{7}{x^{\frac{1}{2}}}} \, dx$

Step 2: Integrate

[Integrand] Rewrite [Exponential Rule - Rewrite]: $\displaystyle \int\limits^{\infty}_{\frac{\pi}{2}} {\frac{7}{x^{\frac{1}{2}}}} \, dx = \int\limits^{\infty}_{\frac{\pi}{2}} {7x^{\frac{-1}{2}}} \, dx$ [Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^{\infty}_{\frac{\pi}{2}} {\frac{7}{x^{\frac{1}{2}}}} \, dx = 7\int\limits^{\infty}_{\frac{\pi}{2}} {x^{\frac{-1}{2}}} \, dx$ [Integral] Rewrite [Improper Integral]: $\displaystyle \int\limits^{\infty}_{\frac{\pi}{2}} {\frac{7}{x^{\frac{1}{2}}}} \, dx = \lim_{b \to \infty} 7\int\limits^b_{\frac{\pi}{2}} {x^{\frac{-1}{2}}} \, dx$ [Integral] Reverse Power Rule: $\displaystyle \int\limits^{\infty}_{\frac{\pi}{2}} {\frac{7}{x^{\frac{1}{2}}}} \, dx = \lim_{b \to \infty} 7(2x^{\frac{1}{2}}) \bigg| \limits^b_{\frac{\pi}{2}}$ [Limit] Rewrite [Limit Property - Multiplied Constant]: $\displaystyle \int\limits^{\infty}_{\frac{\pi}{2}} {\frac{7}{x^{\frac{1}{2}}}} \, dx = 7\lim_{b \to \infty} (2x^{\frac{1}{2}}) \bigg| \limits^b_{\frac{\pi}{2}}$ Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^{\infty}_{\frac{\pi}{2}} {\frac{7}{x^{\frac{1}{2}}}} \, dx = 7\lim_{b \to \infty} (2b^{\frac{1}{2}} - \sqrt{2\pi})$ Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle \int\limits^{\infty}_{\frac{\pi}{2}} {\frac{7}{x^{\frac{1}{2}}}} \, dx = \infty$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer from: Quest

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did not satisfy the given simplify expression.

Answer from: Quest

C, e, and a (hope it )

Another question on Mathematics

Mathematics, 21.06.2019 17:30

25 ! the line of best fit is h = 5a + 86. predict the height at age 16.

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

What is the volume of a cone with a height of 6 cm in the radius of 2 cm

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

The measure of an angle is 117°. what is the measure of a supplementary angle?

Answers: 2

Answer

Mathematics, 21.06.2019 19:30

Needmax recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

Answers: 2

Answer

You know the right answer?

Calculus question, just the first line. other stuff is just my
...

Questions