# How do you find the limit of #x^(sin(x))# as x approaches 0?

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Next bit is unnecessary, see ratnaker-m's note below...

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To find the limit of x^(sin(x)) as x approaches 0, we can use the concept of exponential and trigonometric limits. By applying the limit properties, we can rewrite the expression as e^(ln(x^(sin(x)))). Then, using the properties of logarithms, we can simplify it further to e^(sin(x) * ln(x)).

Next, we can evaluate the limit of sin(x) * ln(x) as x approaches 0. By using the limit properties and the fact that sin(x) approaches 0 as x approaches 0, we can conclude that the limit of sin(x) * ln(x) as x approaches 0 is 0.

Finally, we substitute this result back into the original expression, giving us e^0, which equals 1. Therefore, the limit of x^(sin(x)) as x approaches 0 is 1.

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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 find the limit of #cosx/(x^2+9)# as #x->0#?
- How do you find one sided limits without graph?
- What are the removable and non-removable discontinuities, if any, of #f(x)=(3x^2-7x-6 )/ (x-3 ) #?
- What is the limit as x approaches infinity of #1.001^x#?
- For what values of x, if any, does #f(x) = 1/(xe^x-3) # have vertical asymptotes?

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