1. A pendulum moving in simple harmonic motion is modelled by the function s open parentheses t close parentheses equals negative 5 cos left parenthesis begin inline style fraction numerator pi t over denominator 4 end fraction end style right parenthesis
, where s
is measured in inches and t
is measured in seconds. Determine the first time when the distance moved is 4 inches.
2. Evaluate
limit as x rightwards arrow 5 to the power of minus of space f left parenthesis x right parenthesis
if f left parenthesis x right parenthesis space equals space fraction numerator 1 over denominator left parenthesis x minus 5 right parenthesis to the power of 4 end fraction
.
3. Evaluate
limit as theta rightwards arrow 0 of space f left parenthesis theta right parenthesis
, where f left parenthesis theta right parenthesis equals fraction numerator sin theta minus cos 3 theta over denominator theta times left parenthesis 1 plus cos 2 theta right parenthesis end fraction
.
4. Find the intervals over which the function f left parenthesis x right parenthesis equals fraction numerator 2 x squared plus 3 x plus 1 over denominator x squared minus 5 x end fraction
is continuous.
5. Find a non-zero value for the constant k that makes the function f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator tan space k x over denominator x end fraction comma space end cell row cell 5 x plus 3 comma space end cell end table close open table attributes columnalign right end attributes row cell x less than 0 end cell row cell x greater or equal than 0 end cell end table close curly brackets
continuous at x equals 0
.
6. Determine the value of delta greater than 0
for which limit as x rightwards arrow 4 of left parenthesis 3 x squared minus 1 right parenthesis equals 47 space
.
7. Determine the value of delta greater than 0
for which limit as x rightwards arrow 2 of fraction numerator 1 over denominator left parenthesis x minus 2 right parenthesis squared space end fraction equals infinity
.
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