Calculus 1: Indeterminate Forms and l'Hospital's Rule
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All Calculus 1LimitsDefinition of the DerivativeProduct and Quotient RulePower Rule and Basic DerivativesDerivatives of Trig FunctionsExponential and Logarithmic FunctionsChain RuleInverse and Hyperbolic Trig DerivativesImplicit DifferentiationRelated Rates ProblemsLogarithmic DifferentiationGraphing and Critical PointsOptimization ProblemsIndeterminate Forms and l'Hospital's RuleLinear Approximation and DifferentialsNewton Raphson MethodIndefinite IntegralsU SubstitutionDefinite Integrals and Fundamental TheoremApplications of Integration
Use l'Hospital's Rule to find the following limit
##\lim_{x\rightarrow 1} \frac{x^a - 1}{x^b - 1}##
##\lim_{x\rightarrow 1} \frac{x^a - 1}{x^b - 1}##
Compute the following limit
##\lim_{x\rightarrow 0} \frac{\sin{(5x)}}{x}##
##\lim_{x\rightarrow 0} \frac{\sin{(5x)}}{x}##
Use l'Hospital's Rule to find the limit
##\lim_{x\rightarrow 0} \frac{x^2 - 6x + 2}{x + 1}##
##\lim_{x\rightarrow 0} \frac{x^2 - 6x + 2}{x + 1}##
Evaluate the following limit
##\lim_{x\rightarrow \infty} \frac{\ln{(1 + e^{3x})}}{2x + 5}##
##\lim_{x\rightarrow \infty} \frac{\ln{(1 + e^{3x})}}{2x + 5}##
Explain why the following limit can not be found using l'Hospital's Rule then find the limit using a different method.
##\lim_{x\rightarrow \infty} \frac{x + \cos{(x)}}{x}##
##\lim_{x\rightarrow \infty} \frac{x + \cos{(x)}}{x}##
Evalute ##\lim_{x\rightarrow 0} \frac{x + \cos{(2x)} - e^x}{x}##
Evaluate the following limit
##\lim_{\theta\rightarrow 0} \frac{\tan{(\theta)} - \theta}{\theta - \sin{(\theta)}}##
##\lim_{\theta\rightarrow 0} \frac{\tan{(\theta)} - \theta}{\theta - \sin{(\theta)}}##
Evaluate the following limit
##\lim_{x\rightarrow 0} \frac{\sin{(3x)}}{\sin{(4x)}}##
##\lim_{x\rightarrow 0} \frac{\sin{(3x)}}{\sin{(4x)}}##