How do you evaluate the limit #abs(x^29)/abs(x3)# as x approaches #3#?
By signing up, you agree to our Terms of Service and Privacy Policy
To evaluate the limit of abs(x^29)/abs(x3) as x approaches 3, we can use direct substitution. Plugging in x=3 directly into the expression results in an indeterminate form of 0/0. To resolve this, we can factor the numerator and denominator. The numerator can be factored as (x+3)(x3), and the denominator is simply abs(x3). Canceling out the common factor of (x3), we are left with abs(x+3). Now, we can substitute x=3 into abs(x+3), which gives us abs(3+3) = abs(6) = 6. Therefore, the limit of abs(x^29)/abs(x3) as x approaches 3 is equal to 6.
By signing up, you agree to our Terms of Service and Privacy Policy
To evaluate the limit ( \frac{x^2  9}{x  3} ) as ( x ) approaches 3, we consider the behavior of the function as ( x ) approaches 3 from both the left and the right sides.

As ( x ) approaches 3 from the left (( x < 3 )):
 Substitute values slightly less than 3 into the function to observe the trend.

As ( x ) approaches 3 from the right (( x > 3 )):
 Substitute values slightly greater than 3 into the function to observe the trend.

Compare the results from both sides to determine if the limit exists.
Let's evaluate:

As ( x ) approaches 3 from the left (( x < 3 )):
 Substitute ( x = 2.9 ): ( \frac{2.9^2  9}{2.9  3} = \frac{8.41  9}{0.1} = \frac{0.59}{0.1} = 5.9 ).

As ( x ) approaches 3 from the right (( x > 3 )):
 Substitute ( x = 3.1 ): ( \frac{3.1^2  9}{3.1  3} = \frac{9.61  9}{0.1} = \frac{0.61}{0.1} = 6.1 ).
Since the limit from the left side (5.9) is not equal to the limit from the right side (6.1), the limit as ( x ) approaches 3 does not exist.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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 onesided 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 onesided 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 onesided 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 #f(x)=(secx1)/x^2# as x approaches 0?
 How do you evaluate the limit of #x+sinx# as #x>0#?
 For what values of x, if any, does #f(x) = 1/((x2)(x1)(e^x3)) # have vertical asymptotes?
 How do you use the Squeeze Theorem to find #lim (arctan(x) )/ (x)# as x approaches infinity?
 How do you evaluate #(sin^3x+cos^3x )/( cosx + sinx)# as x approaches #3pi/4#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7