# How do you find the limit of # (5^t-3^t)/t# as t approaches 0?

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

We know that,

Let ,

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

To find the limit of (5^t - 3^t)/t as t approaches 0, we can use L'Hôpital's rule. Taking the derivative of the numerator and denominator separately, we get (ln(5)*5^t - ln(3)*3^t)/(1). Evaluating this expression as t approaches 0, we have (ln(5) - ln(3))/1, which simplifies to ln(5) - ln(3). Therefore, the limit is ln(5) - ln(3).

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.

- How do you prove that the limit of # (x^3*y^2)/(x^2+y^2)# as (x,y) approaches (0,0) using the epsilon delta proof?
- What exactly is a limit in calculus?
- How do you find the limit of #cos(x)/(x - pi/2) # as x approaches pi/2?
- What is the limit as x approaches 0 of #2x^6 + 6x^3#?
- What is the limit of #root3[x^3+2] - root3[x^3-1]# as x goes to infinity?

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