# Determining Limits Algebraically

Determining limits algebraically is a fundamental concept in calculus that allows us to understand the behavior of functions as they approach certain values or points. By employing algebraic techniques such as factoring, rationalizing, and simplifying expressions, we can evaluate limits without necessarily needing to graph the function. This approach enables us to analyze functions in more abstract and general terms, providing insights into their behavior without relying solely on graphical representations. Mastering the algebraic methods for determining limits is essential for tackling more complex problems in calculus and other branches of mathematics.

Questions

- If limit of #f(x)=4# as #x->c#, what the limit of #3f(x)# as #x->c#?
- How do you evaluate the limit #15/(t^2+5)# as t approaches #1#?
- How do you find the limit of #((t^2)+(5t)) / (cosh(t)-1)# as t approaches 0?
- How do you evaluate #(sin2h*sin3h) /( h^2)# as h approaches 0?
- How do you evaluate each of the following limits, if it exists #lim (3x^2+5x-2)/(x^2-3x-10)# as #x-> -2#?
- How do you find the limit of #sin(costheta)/sectheta# as #theta->0#?
- How do you determine the limit of #(x)/sqrt(x^2-x)# as x approaches infinity?
- How do you evaluate the limit #(3x^4-x^2+5)/(10-2x^4)# as x approaches #oo#?
- How do you determine the limit of #(pi/2)-(x)/(cos(x))# as x approaches pi/2?
- If limit of #f(x)=27# as #x->c#, what the limit of #f(x)/18# as #x->c#?
- How do you find the limit of #(x(1-cosx))/tan^3x# as #x->0#?
- How do you evaluate # x^(ln(7)/(1+ln(x)) # as x approaches infinity?
- What is the limit of #(1+4/x)^x# as x approaches infinity?
- How do you find the limit #cosx/(pi/2-x)# as #x->pi/2#?
- How do you evaluate limits of # lim 9/(x-3)^2# where x-3?
- What is the limit of #(cos(3x)-cos(4x))/x^2# as x approaches #oo#?
- Find the limit? lim x#rarr# #oo# #(10x^5+x^4+31)/(x^6)#
- #lim_(h->0) [sin(2π+h) - sin(2π)]/h =# ?
- How do you find the limit of #(sqrt(x+8)-3)/(x-1)# as #x->1#?
- If limit of #f(x)=27# as #x->c#, what the limit of #(f(x))^(3/2)# as #x->c#?