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Find
lim_(h rarr0)(4sin((pi)/(2)+h)-4sin((pi)/(2)))/(h).
Choose 1 answer:
(A) 0
(B) 1
(C) 4
D The limit doesn't exist

Find $\lim _{h \rightarrow 0} \frac{4 \sin \left(\frac{\pi}{2}+h\right)-4 \sin \left(\frac{\pi}{2}\right)}{h}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $0$ $\newline$ (B) $1$ $\newline$ (C) $4$ $\newline$ (D) The limit doesn't exist

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Solve quadratic inequalities

Full solution

Q. Find

\lim _{h \rightarrow 0} \frac{4 \sin \left(\frac{\pi}{2}+h\right)-4 \sin \left(\frac{\pi}{2}\right)}{h}

.

\newline

Choose

1

answer:

\newline

(A)

0

\newline

(B)

1

\newline

(C)

4

\newline

(D) The limit doesn't exist

Identify Limit: Identify the limit to solve: $\lim_{h \to 0}\frac{4\sin\left(\frac{\pi}{2}+h\right)-4\sin\left(\frac{\pi}{2}\right)}{h}$ .
Recognize Sin Value: Recognize that $\sin\left(\frac{\pi}{2}\right) = 1$ , so $4\sin\left(\frac{\pi}{2}\right) = 4$ .
Substitute Sin Value: Substitute $\sin\left(\frac{\pi}{2}\right)$ with $1$ in the expression: $\lim_{h \to 0}\left(\frac{4\sin\left(\frac{\pi}{2}+h\right)-4}{h}\right)$ .
Apply Limit to Sine: Apply the limit to the sine function directly: $\lim_{h \to 0}\frac{4(\sin(\frac{\pi}{2}+h)-1)}{h}.$
Use Approximation: Use the fact that $\sin\left(\frac{\pi}{2}+h\right)$ is approximately $1$ when $h$ is close to $0$ : $\lim_{h \rightarrow 0}4\left(1-1\right)/h$ .

More problems from Solve quadratic inequalities

Question

The Smiths and the Johnsons were competing in the final leg of the Amazing Race. In their race to the finish, the Smiths immediately took off on a

165

kilometer path traveling at an average speed of

v

kilometers per hour.

\newline

The Johnsons' start was delayed by

\frac{1}{2}

hour. Eventually, they took a

180

kilometer path to the finish, traveling at an average speed that was

20

kilometers per hour faster than the Smiths' speed.

\newline

The Johnsons arrived at the finish line first and won the race!

\newline

Write an inequality in terms of

v

that models the situation.

Posted 3 months ago

Question

-10 x-3 \geq 8 x+4

\newline

Which of the following best describes the solutions to the inequality shown?

\newline

1

\newline

x \leq-\frac{7}{18}

\newline

x \leq-\frac{7}{2}

\newline

x \leq-\frac{1}{18}

\newline

x \geq-\frac{7}{18}

Posted 3 months ago

Question

-12 x<-72

\newline

Which of the following best describes the solutions to the inequality shown?

\newline

1

\newline

x<6

\newline

x>6

\newline

x<\frac{1}{6}

\newline

x>\frac{1}{6}

Posted 3 months ago

Question

8 x+6<4 x+10

\newline

Which of the following best describes the solutions to the inequality shown?

\newline

1

\newline

x<\frac{1}{3}

\newline

x<4

\newline

x<1

\newline

x>1

Posted 3 months ago

Question

6 x-2<2 x+3

\newline

Which of the following best describes the solutions to the inequality shown?

\newline

1

\newline

x<\frac{5}{4}

\newline

x>\frac{5}{4}

\newline

x<\frac{1}{4}

\newline

x<\frac{5}{8}

Posted 3 months ago

Question

16<-4 x

\newline

Which of the following best describes the solutions to the inequality shown?

\newline

1

\newline

x<-4

\newline

x>-4

\newline

x<-\frac{1}{4}

\newline

x>-\frac{1}{4}

Posted 3 months ago

Question

-2>\frac{3(b+4)}{-2}

\newline

Which of the following best describes the solutions to the inequality shown?

\newline

1

\newline

b<-3

\newline

b<-\frac{16}{3}

\newline

b>-\frac{8}{3}

\newline

b>0

Posted 3 months ago

Question

\lim _{x \rightarrow 4} \frac{2-\sqrt{4 x-12}}{x-4}

\newline

1

\newline

2

\newline

1

\newline

-1

\newline

(D) The limit doesn't exist

Posted 3 months ago

Question

\lim _{x \rightarrow 2} \frac{x^{4}-4 x^{3}+4 x^{2}}{x-2}

\newline

1

\newline

-4

\newline

0

\newline

4

\newline

(D) The limit doesn't exist

Posted 3 months ago

Question

f

be a continuous function on the closed interval

[-5,0]

f(-5)=0

f(0)=5

\newline

Which of the following is guaranteed by the Intermediate Value Theorem?

\newline

1

\newline

f(c)=-2

for at least one

c

0

5

\newline

f(c)=2

for at least one

c

0

5

\newline

f(c)=-2

for at least one

c

-5

0

\newline

f(c)=2

for at least one

c

-5

0

Posted 3 months ago