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Find 
lim_(x rarr0)g(x) for 
g(x)=(4x^(2)-15)/(4x+3)

Find limx0g(x) \lim _{x \rightarrow 0} g(x) for g(x)=4x2154x+3 g(x)=\frac{4 x^{2}-15}{4 x+3}

Full solution

Q. Find limx0g(x) \lim _{x \rightarrow 0} g(x) for g(x)=4x2154x+3 g(x)=\frac{4 x^{2}-15}{4 x+3}
  1. Identify the function: Identify the function g(x)g(x) that we are finding the limit for as xx approaches 00. The function is g(x)=4x2154x+3g(x) = \frac{4x^2 - 15}{4x + 3}.
  2. Check direct substitution: Check if direct substitution of x=0x = 0 into g(x)g(x) results in an indeterminate form. Substituting x=0x = 0 into g(x)g(x) gives g(0)=(15)/(3)=5g(0) = (-15) / (3) = -5, which is a determinate value.
  3. Evaluate limit at x=0x=0: Since direct substitution does not result in an indeterminate form, the limit of g(x)g(x) as xx approaches 00 is simply the value of g(x)g(x) when xx is 00.
  4. Conclude the limit: Conclude that the limit of g(x)g(x) as xx approaches 00 is 5-5.

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