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Olin [163]
3 years ago
7

Use the table for each problem to find the given limits.

Mathematics
1 answer:
asambeis [7]3 years ago
4 0

Answer:

1) \lim_{x \to3  } (2f(x))+g(-x))=13

2) \lim_{x \to3  }\frac{g(x)}{f(-x)}=1/2

Step-by-step explanation:

So we are given the limits:

\lim_{x \to3 }f(x)=4\text{ and }  \lim_{x \to-3 } f(x)=2

And:

\lim_{x \to 3 } g(x)= 1\text{ and }  \lim_{x \to -3 } g(x)=5

Question A)

We have the limit:

\lim_{x \to3  } (2f(x))+g(-x))

We can split this limit using our properties:

= \lim_{x \to 3} (2f(x))+\lim_{x \to 3} g(-x)

Now, use direct substitution. Substitute 3 for x. So:

=2(f(3))+g(-3)

We are given that f(3) (or the limit as x approaches towards 3) is 4.

We know that the limit as x tends towards -3 of g(x) is 5. In other words, g(-3) can be said to be 5. So:

=2(4)+(5)

Multiply:

=8+5=13

So, our limit is:

\lim_{x \to3  } (2f(x))+g(-x))=13

Question B:

We have the limit:

\lim_{x \to3  }\frac{g(x)}{f(-x)}

Again, we can rewrite this as:

\frac{\lim_{x \to3  }g(x)}{\lim_{x \to3  }f(-x)}}

Direct substitution:

=\frac{g(3)}{f(-3)}

The value in the numerator, as given, is 1.

The value in the denominator will be 2. So:

=1/2

Therefore, our limit is:

\lim_{x \to3  }\frac{g(x)}{f(-x)}=1/2

And we're done!

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2z -5(z +2) = -8 - 2z<br><br> Please explain!! Thank you
Korolek [52]

Follow PEMDAS.

You would first do your distributive property which is, -5(z+2). You would multiply -5 to z and -5 to 2 which will give you -5z + -10.

so now you have 2z-5z+ -10= -8 - 2z. Now you must isolate the variable. So subtract -8 to -10 which will give you -18.

Now you have the equation 2z-5z-18=-2z

Now combine like terms. 2z-5z= -3z

Now you have the equation -3z-18=-2z

Now you must move the -3z to the other side of the equal sign by adding the opposite which is +3z to -2z which will give you +1z

Now you have -18= 1z

Now you divide. -18 divided by 1 is -18.

So your final answer will be -18=z

7 0
3 years ago
An exam worth 145 points contains 50 questions. The number of two-point questions is equal to 50 minus the number of five-point
abruzzese [7]

Answer:

Therefore there are 35 number of 2-point questions and 15 number of 5-point questions.

Step-by-step explanation:

i) let the number of 2 point question is x.

ii) let the number of 5 point questions be y

iii) total number of questions is 50

iv) therefore x + y = 50

v) it is also given that 2x + 5y = 145

vi) solving for the two equations found in iv) and v). Multiplying iv) by 2 we get

    2x + 2y = 100

vii) subtracting equation vi) from equation v) we get 3y = 45.

viii) Therefore y = 15.

ix) using the value in viii) and substituting in iv) we get x + 15 = 50.

    Therefore x = 50 - 15  = 35

x) Therefore there are 35 number of 2-point questions and 15 number of 5-point questions.

3 0
3 years ago
Read 2 more answers
Carrie and brent leave home at the same time. carrie drives due east at a rate of 30 mph, while brent drives due south at a rate
Helga [31]

<h3>They are 268 miles far apart after 4 hours</h3>

<h3>Further explanation</h3>

Acceleration is rate of change of velocity.

\large {\boxed {a = \frac{v - u}{t} } }

\large {\boxed {d = \frac{v + u}{2}~t } }

<em>a = acceleration ( m/s² )</em>

<em>v = final velocity ( m/s )</em>

<em>u = initial velocity ( m/s )</em>

<em>t = time taken ( s )</em>

<em>d = distance ( m )</em>

Let us now tackle the problem !

<u>Given :</u>

v₁ = 30 mph due east

v₂ = 60 mph due south

t = 4 hours

<u>Unknown :</u>

displacement = d = ?

<u>Solution :</u>

d_1 = v_1 \times t

d_1 = 30 ~ mph \times 4 ~ h

d_1 = \boxed {120 ~ miles}

d_2 = v_2 \times t

d_2 = 60 ~ mph \times 4 ~ h

d_2 = \boxed {240 ~ miles}

d^2 = (d_1)^2 + (d_2)^2

d^2 = 120^2 + 240^2

d^2 = 72000

d = \sqrt{72000}

d = 120\sqrt{5} ~ miles

d \approx \boxed {268 ~ miles}

<h2>Conclusion :</h2><h3>They are 268 miles far apart after 4 hours</h3>

<h3>Learn more</h3>
  • Velocity of Runner : brainly.com/question/3813437
  • Kinetic Energy : brainly.com/question/692781
  • Acceleration : brainly.com/question/2283922
  • The Speed of Car : brainly.com/question/568302

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate

6 0
3 years ago
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How many 15° angles are in a circle?<br> Enter your answer in the box.<br> angles
Alex_Xolod [135]

Answer:

24

Step-by-step explanation:

a circle is 360

we can divide 360 by 15

360 divided by 15 =

24

5 0
2 years ago
-12-6-(-2) combine like terms
dexar [7]

Answer:

-12-6-(-2)

-12-6-+2

-18+2

-16

Hope This Helps!!!

8 0
2 years ago
Read 2 more answers
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