1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
jonny [76]
3 years ago
9

Use the definition of continuity and the properties of limits to show that the function f(x) = x^2 + 5(x - 2)^7 is continuous at

x = 3
Mathematics
1 answer:
frosja888 [35]3 years ago
6 0

Answer:

See below.

Step-by-step explanation:

First check that f(x) has a real value at x = 3:

f(3) = 3^2 + 5(3 - 2)^7

=  9 + 5 * 1^7

=  14,

So the first condition is met.

Now we check if limit as x approaches 3 exists.

As x approaches 3 from below f(x) approaches 14 and at x = 3 = 14.

As x approaches 3 from above f(x) approaches 14 and at x = 3 = 14.

These 3 conditions  shows that f(x) is continuous at x = 3.

You might be interested in
How many times does 1/4 go into 3/8?
Luba_88 [7]
3/8 divided by 1/4

hope this helped
5 0
3 years ago
Read 2 more answers
Solve the equation. 12x+3=51
Zinaida [17]

12x + 3 = 51 \\ 12x = 48 \\ x = 4

3 0
3 years ago
1. A point at (3, 2) is rotated 180° clockwise about the origin.
luda_lava [24]
1.) (-3,-2)
2.) 8.4m^3
3.) 37.7m^3
6 0
3 years ago
A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = −16t2 + 48t where t equals the
zlopas [31]
1. The function h(t)=-16t^{2}+48t is a parabola of the form ax^{2}+bx. The the formula for the axis of symmetry of a parabola is x= \frac{-b}{2a}. We can infer from our function that a=-16 and b=48, so lets replace those values in our formula:
x= \frac{-b}{2a}
x= \frac{-48}{-2(16)}
x= \frac{-48}{-32}
x= \frac{3}{2}
x=1.5
We can conclude that to the left of the line of symmetry the ball is reaching its maximum height, and to the right of the line of symmetry the ball is falling.

2. Lets check how much time the ball takes to reach its maximum height and return to the ground. To do that we are going to set the height equal to zero:
0=-16t^{2}+48t
-16t(t-3)=0
t=0 or t-3=0
t=0 or t=3
From our previous point we know that the ball reaches its maximum time at t=1.5, which means that <span>it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.</span>

7 0
3 years ago
Read 2 more answers
Sunday elementary school is having its annual Read a thon. the third graders have read 573 books so fair. Their goal is to read
il63 [147K]
The answer would be 901 because they said what is the least number they would need to read and their goal is MORE than 900. The amount of books that they already had is useless information (Ignore). They love giving trick questions. :)
4 0
3 years ago
Other questions:
  • in the calculations shown, what will the units of the final answer be? 18 meters/second x 3600 secons/1 hour x 1 mile/ 1609meter
    12·1 answer
  • The Juarez family is making a cross- country trip on Saturday they traveled 450.8 miles on Sunday they traveled 604.6 miles how
    12·1 answer
  • Pls help me answer 10, 11, and 12 thx in advance
    13·1 answer
  • 13 × 11 + 3/4 × 3/5 + 13 × 3/4 + 11 × 3/5
    7·1 answer
  • What is the image of the point (-8,0) after a rotation of 270° counterclockwise
    13·2 answers
  • If f(x) = -2x2 + x – 5, what is f(3)?
    15·1 answer
  • The true length of recovery for patients with knee surgery is normally distributed with a mean of 123 days and a standard deviat
    15·1 answer
  • HELP PLEASE!!!!! ASAP
    8·1 answer
  • Which is 1/3+1/4???
    7·2 answers
  • Helppppppp plzzzzzzz
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!