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Alex_Xolod [135]
3 years ago
10

Find the indicated limit, if it exists.(7 points)

Mathematics
1 answer:
Alecsey [184]3 years ago
7 0

Answer:

7

Step-by-step explanation:

The left hand limit is when we approach zero from left. We use the function on this domain in finding the limit.

\lim_{x \to 0^-} f(x)=7-x^2

\lim_{x \to 0^-} f(x)=7-(0)^2=7

The right hand limit is

\lim_{x \to 0^+} f(x)=10x+7

\lim_{x \to 0^+} f(x)=10(0)+7=7

Since the left hand limit equals the right hand limit;

\lim_{x \to 0} f(x)=7

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I need help quick- Thanks btw :>
saul85 [17]

Answer: 3/4 feet

Step-by-step explanation:Conversion a mixed number 3 5/

12

to a improper fraction: 3 5/12 = 3 5/

12

= 3 · 12 + 5/

12

= 36 + 5/

12

= 41/

12

To find new numerator:

a) Multiply the whole number 3 by the denominator 12. Whole number 3 equally 3 * 12/

12

= 36/

12

b) Add the answer from previous step 36 to the numerator 5. New numerator is 36 + 5 = 41

c) Write a previous answer (new numerator 41) over the denominator 12.

Three and five twelfths is forty-one twelfths

Conversion a mixed number 2 2/

3

to a improper fraction: 2 2/3 = 2 2/

3

= 2 · 3 + 2/

3

= 6 + 2/

3

= 8/

3

To find new numerator:

a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/

3

= 6/

3

b) Add the answer from previous step 6 to the numerator 2. New numerator is 6 + 2 = 8

c) Write a previous answer (new numerator 8) over the denominator 3.

Two and two thirds is eight thirds

Subtract: 41/

12

- 8/

3

= 41/

12

- 8 · 4/

3 · 4

= 41/

12

- 32/

12

= 41 - 32/

12

= 9/

12

= 3 · 3/

3 · 4

= 3/

4

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of the both denominators - LCM(12, 3) = 12. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 12 × 3 = 36. In the next intermediate step , cancel by a common factor of 3 gives 3/

4

.

5 0
2 years ago
A​ hot-air balloon is 160 ftabove the ground when a motorcycle​ (traveling in a straight line on a horizontal​ road) passes dire
Charra [1.4K]

Answer:

73.77 ft/s

Step-by-step explanation:

Let's imagine this situation as a right triangle where the distance between the two points is the hypotenuse.

-Applying Pythagoras theorem:

z^2=x^2+y^2\\\\z=\sqrt{x^2+y^2}\\\\x=dx*t+x_i, x_i=0\\\\y=dy*t+y_i\\\\y_i=160\ ft

#Take the derivative of the first equation and solve for dz:

d(z^2=x^2+y^2)\\\\2z*dz=2x*dx+2y*dy\\\\dz=\frac{x*dx+y*dy}{z}\\\\dz=\frac{x*dx+y*dy}{\sqrt{x^2+y^2}}\\\\\\dz=\frac{dx^2*t+dy(dy*t+160)}{\sqrt{(dx*t)^2+(dy*t)}}

#We then substitute the values given in the question to solve for dz:

dz=\frac{7*66^2+14(14*7+160)}{\sqrt{(66*7)^2+7*14+160}}\\\\=73.78

Hence, the rate of change of the distance between the motorcycle and the balloon 7 seconds ​later is 73.77 ft/s

3 0
3 years ago
Help please !<br><br> I’ll mark brainliest:)
sashaice [31]
<span>The answer is $4,955.30</span>
7 0
3 years ago
Four friends are standing in line to buy tickets. Carlos is not first in line.Paige is ahead of of Kate.Lisa is last in line.Who
iren2701 [21]
Paige is ahead of kate. It dosen't say she is behind anyone or last in the line. Carlos is not first in line. Kate cannot be first because someone is ahead of her. And lisa is last. So the answer is definitely paige. Hope i helped. Have a nice day. 
4 0
3 years ago
Read 2 more answers
1. En una tienda de ropa se pusieron en oferta guantes y chamarras. El primer dia se vendieron 6 pares
Softa [21]
10560 so much money all forget to count
6 0
2 years ago
Read 2 more answers
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