How do you prove that #g(x) = 1/2x# is continuous at #x=1/4#?

Answer 1

Please refer to the Explanation.

To prove that the function #g(x)=1/2x# is continuous at #x=1/4,# we
have to show that, #lim_(x to 1/4) g(x)=g(1/4).#
Now, #lim_(x to 1/x) g(x),#
#=lim_(x to 1/4) 1/2x,#
#=1/2*1/4,#
#=1/8,#
#=g(1/4).#
Hence, #g# is continuous at #x=1/4.#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To prove that g(x) = 1/2x is continuous at x=1/4, we need to show that the limit of g(x) as x approaches 1/4 exists and is equal to g(1/4).

First, let's find the limit of g(x) as x approaches 1/4:

lim(x→1/4) (1/2x) = 1/2 * (lim(x→1/4) 1/x)

Next, we evaluate the limit of 1/x as x approaches 1/4:

lim(x→1/4) 1/x = 1/(1/4) = 4

Therefore, the limit of g(x) as x approaches 1/4 is 4.

Now, let's find g(1/4):

g(1/4) = 1/2 * (1/4) = 1/8

Since the limit of g(x) as x approaches 1/4 (which is 4) is equal to g(1/4) (which is 1/8), we can conclude that g(x) = 1/2x is continuous at x=1/4.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7