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Find the variable to make the function continuous

  • Thread starter Painguy
  • Start date
  • #1
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Homework Statement


Find k so that the following function is continuous on any interval.

j(x) = {k cos(x), x ≤ 0
{10ex − k, 0 < x

Homework Equations




The Attempt at a Solution


I originally thought i had to check if the limits of both parts of the functions existed, and if so to set them equal to each other, but then I reread the question and realized that it wasn't asking me if its continuous, but to make it continuous by finding the value of k. I figured that i might be able to to set the two functions equal to each other to see if I can get k, but I'm not sure if that's right or not.
 

Answers and Replies

  • #2
Ray Vickson
Science Advisor
Homework Helper
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Homework Statement


Find k so that the following function is continuous on any interval.

j(x) = {k cos(x), x ≤ 0
{10ex − k, 0 < x

Homework Equations




The Attempt at a Solution


I originally thought i had to check if the limits of both parts of the functions existed, and if so to set them equal to each other, but then I reread the question and realized that it wasn't asking me if its continuous, but to make it continuous by finding the value of k. I figured that i might be able to to set the two functions equal to each other to see if I can get k, but I'm not sure if that's right or not.
For x > 0 do you mean 10*e*x - k, or do you mean 10*ex - k?

RGV
 
  • #3
Bacle2
Science Advisor
1,089
10

Homework Statement


Find k so that the following function is continuous on any interval.

j(x) = {k cos(x), x ≤ 0
{10ex − k, 0 < x

Homework Equations




The Attempt at a Solution


I originally thought i had to check if the limits of both parts of the functions existed, and if so to set them equal to each other, but then I reread the question and realized that it wasn't asking me if its continuous, but to make it continuous by finding the value of k. I figured that i might be able to to set the two functions equal to each other to see if I can get k, but I'm not sure if that's right or not.

Maybe to give a 100% answer, just state that right of zero and left of zero there are

no problems of continuity. Then , also, f is continuous if the value at a point coincides

with the right- and left- limits.
 
  • #4
120
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For x > 0 do you mean 10*e*x - k, or do you mean 10*ex - k?

RGV
I'm sorry i meant 10*ex - k
 
  • #5
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,219
945

Homework Statement


Find k so that the following function is continuous on any interval.

j(x) = {k cos(x), x ≤ 0
{10ex − k, 0 < x

Homework Equations



The Attempt at a Solution


I originally thought i had to check if the limits of both parts of the functions existed, and if so to set them equal to each other, but then I reread the question and realized that it wasn't asking me if its continuous, but to make it continuous by finding the value of k. I figured that i might be able to to set the two functions equal to each other to see if I can get k, but I'm not sure if that's right or not.
Chose k to make the following two limits equal to each other.

[itex]\lim_{x\to0^+}\,j(x)\,,[/itex] this is where j(x) = 10ex − k .

[itex]\lim_{x\to0^-}\,j(x)\,,[/itex] this is where j(x) = k cos(x) .

Then make sure that those limits equal j(0) (which of course, they will).
 
  • #6
120
0
I see. That helps. That's what i intended to to at first, but im not sure how i misinterpreted the question. Anyway thanks for all your help guys
 

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