# How do you evaluate #(3x^2+2x+sinx)/(sinx+e^3x-1)# as x approaches 0?

NB note the red correction, is there a typo in the question cos it looks odd to me?!?!

start by plugging on x = 0 to see what it looks like

that's

so that 's

Again we can pop in x = 0 to see where we are

that's

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

To evaluate the expression (3x^2+2x+sinx)/(sinx+e^3x-1) as x approaches 0, we can substitute 0 for x in the expression. This gives us (3(0)^2+2(0)+sin(0))/(sin(0)+e^3(0)-1). Simplifying further, we have (0+0+0)/(0+1-1). Continuing to simplify, we get 0/0. However, this is an indeterminate form. To evaluate it further, we can use L'Hôpital's rule. Taking the derivative of the numerator and denominator separately, we get (6x+2+cosx)/(cosx+3e^3x). Substituting x=0 into this derivative expression, we have (6(0)+2+cos(0))/(cos(0)+3e^3(0)). Simplifying, we get (2+1)/(1+3). Therefore, the limit of the expression as x approaches 0 is 3/4.

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.

- What is the limit of #cosx# as x goes to infinity?
- If limit of #f(x)=3/2# and #g(x)=1/2# as #x->c#, what the limit of #f(x)+g(x)# as #x->c#?
- How do you prove that the limit of #(x^2 - x) = 0 # as x approaches 1 using the epsilon delta proof?
- How do you find the limit of #sqrt(3+x) - sqrt(3)/x # as x approaches 0?
- How do you determine the limit of #csc x# as x approaches #oo#?

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