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3 years ago

!! AP CALCULUS AB !! find the limit of [(secxsinx) + (cscxcosx)]/(3secx) as x approaches 3pi/2

Mathematics

1 answer:

uysha [10]3 years ago

6 0

$f(x)= \frac{\frac{\sin{x}}{\cos{x}}+\frac{\cos{x}}{\sin{x}}}{3\sec{x}}$

$\frac{\frac{\sin{x}}{\cos{x}}+\frac{\cos{x}}{\sin{x}}}{3\sec{x}} \implies \\ \frac{\sin^2{x}+\cos^2{x}}{\sin{x}\cos{x}}\frac{\cos{x}}{3}\implies \\\frac{1}{\sin{x}\cos{x}}*\frac{\cos{x}}{3}\implies \\ \frac{1}{3\sin{x}}$

So,

$\lim_{x \rightarrow \frac{3\pi}{2}}{f(x)=f(\frac{3\pi}{2})=\frac{1}{3\sin{\frac{3\pi}{2}}}=-\frac{1}{3}$

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Urgent, please i will give brainliest

Ne4ueva [31]

Answer:

1. $\frac{\sqrt{13} }{3}$

2. 3.2362

3. $\frac{60}{11}$

Step-by-step explanation:

Cot is the trigonometric ratio defined by "adjacent" over "opposite". So, adjacent = 2 and opposite = 3.

By pythagorean theorem, we have the "hypotenuse" as $\sqrt{2^2+3^2}=\sqrt{13}$

Csc is defined as the trig ratio "hypotenuse" over "opposite". We know the sides, so Csc $\theta$ = $\frac{\sqrt{13} }{3}$

First answer choice is right.

By definition, Csc $\theta$ is the inverse of Sine $\theta$ . If given the value of sin theta, to find value of csc theta, we take the reciprocal of it. Hence:

$Csc\theta=\frac{1}{0.3090}\\=3.2362$

Third answer choice is right.

By definition tan and cot are inverse of each other. So the value of tan is the reciprocal of the value of cot. We can simply "flip" the value of tan theta to get the value of cot theta. Hence:

$Cot\theta=\frac{60}{11}$

Third answer is right.

3 0

3 years ago

Read 2 more answers

2 (2f+2)= help me fast

8_murik_8 [283]

Distribute

2 × 2f + 2 × 2

Simplify 2 × 2f to 4f

4f + 2 × 2

Simplify 2 × 2 to 4

4f + 4

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2 years ago

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In a group of eighteen people, each person shakes hands once with each other person in the group. How many handshakes will occur

miv72 [106K]

The number of handshakes that will occur in a group of eighteen people if each person shakes hands once with each other person in the group is 153 handshakes

In order to determine the number of handshakes that will occur among 18 people, that is, the number of ways we can choose 2 persons from 18 people.

∴ The number of handshakes = $^{18}C_{2}$

$^{18}C_{2} = \frac{18!}{(18-2)!2!}$

$^{18}C_{2} = \frac{18!}{16!2!}$

$^{18}C_{2} = \frac{18\times17\times16!}{16!\times2!}$

$^{18}C_{2} = \frac{18\times17}{2\times1}$

$^{18}C_{2} = \frac{306}{2}$

$^{18}C_{2} = 153$

∴ The number of handshakes = 153 handshakes

Hence. 153 handshakes will occur in a group of eighteen people if each person shakes hands once with each other person in the group.

Learn more here: brainly.com/question/1991469

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1 year ago

Juniper wants to make a new rectangular garden in her backyard that has a length that is 2 more than twice the width. She needs

lisabon 2012 [21]

Answer:

2x+2y ≤ 64

x=2y+2

Step-by-step explanation:

x = length

y = width

the length is 2 more than twice the width or 2 more than twice y

x = 2+2y

the perimeter of the garden = 2 times the length + 2 times the width

she have 64ft of wire so the perimeter should be equal or less than 64 ft

64 ≥ 2x + 2y

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2 years ago

Area of a regular hexagon with a base of 10 and an apothem of 12

Katen [24]

Draw a regular hexagon. Connect the center to each of the six vertices. Thus, you have six triangles, each with base 10.. The apothem is the height of each triangle. Then the area of each triangle is (1/2)(10)(12) = 60. You have six triangles so the aarea of the hexagon is 6*60 = 360.

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3 years ago

!! AP CALCULUS AB !! find the limit of [(secx*sinx) + (cscx*cosx)]/(3secx) as x approaches 3pi/2

!! AP CALCULUS AB !! find the limit of [(secxsinx) + (cscxcosx)]/(3secx) as x approaches 3pi/2