Calculus 1: Linear Approximation and Differentials
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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
Let ##f(x) = \ln{(x)}## Find the linearization of ##f## at ##1## and use it to evaluate ##\ln{(0.9)}##
Find the linearization of ##f(x) = {(1 + x)}^{P}## at ##0##, and approximate ##f(\sqrt{0.99})##
Suppose that a spherical container has a radius of ##1 \pm 0.001 m##. Approximate the corresponding possible error in the calculated volume.
Use linear approximations to estimate ##\sqrt{8}##. Also find the error and percentage error.
Find the linearization of ##\csc{x}## at ##x = \frac{\pi}{4}## and use it to approximate ##\csc{1}##. Also find the error and percentage error.
Find the local linearization of ##\ln{(x)}## at ##x = e^2## and use it to approximate ##\ln{(7.4)}##. Also find the error and percentage error.
Approximate ##f(x) = \sqrt[3]{x}## at ##x = 26##
Let ##f(x) = \sqrt{x}## at ##x = 4## and ##\Delta{x} = 0.02##
Find ##dx##, ##dy##, ##\Delta{y}##
Find ##dx##, ##dy##, ##\Delta{y}##
Given a circle with a circumference of 56 inches with an error of ##\pm{1.2}## inches. Find the percent error of the area of the circle.
A 12 by 12 square is produced with an error of ##\pm{\frac{1}{64}}## inches in the length of each side. Find the the percent error in the area of one of these squares.