How do you prove that the function #f(x) = x^2 -3x +5# is continuous at a =2?
Prove using limit definition of continuity...
Any polynomial function is continuous everywhere, but let's prove this particular example using the limit definition of continuity...
In our example:
By signing up, you agree to our Terms of Service and Privacy Policy
To prove that the function f(x) = x^2 - 3x + 5 is continuous at a = 2, we need to show that the limit of f(x) as x approaches 2 is equal to f(2).
First, let's find the limit of f(x) as x approaches 2.
lim(x→2) (x^2 - 3x + 5) = (2^2 - 3(2) + 5) = (4 - 6 + 5) = 3
Next, let's find f(2) by substituting x = 2 into the function.
f(2) = (2^2 - 3(2) + 5) = (4 - 6 + 5) = 3
Since the limit of f(x) as x approaches 2 is equal to f(2), we can conclude that the function f(x) = x^2 - 3x + 5 is continuous at a = 2.
By signing up, you agree to our Terms of Service and Privacy Policy
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.
- How do you use the epsilon delta definition to prove that the limit of #2x-4=6# as #x->1#?
- How do you find the limit of #(x/(x+1))^x# as x approaches infinity?
- How do you find the limit of #(sqrt(1+2x))-(sqrt(1-4x)] / x# as x approaches 0?
- How do you find #lim (3x)/(4x-10)# as #x->-oo#?
- How do you evaluate the limit #3x^2+4x-5# as x approaches #5#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7