calculus

Questions1-7.docx

Home >Mathematics homework help >Calculus homework help >calculus

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 is measured in inches and 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 $limit as x rightwards arrow 2 of fraction numerator 1 over denominator left parenthesis x minus 2 right parenthesis squared space end fraction equals infinity$ .

PICK THE CORRECT ANSWER