De Anza College Calculus Definition of Limit Tangent Line Problems Be sure to show work to justify your answers, and simplify your answers. Project 1 Rubr

De Anza College Calculus Definition of Limit Tangent Line Problems Be sure to show work to justify your answers, and simplify your answers.

Project 1 Rubric

Criteria Ratings Pts

This criterion is linked to a learning outcome#1Evaluation of limits showing ALL work to justify the answers

6.0 Pts

Full marks

4.0 Pts

Almost there

Small mistakes or missing steps

2.0 Pts

A good start

0.0 Pts

No marks

6.0 pts

This criterion is linked to a learning outcome#2Must include both preliminary analysis and formal proof

7.0 Pts

Full marks

0.0 Pts

No marks

7.0 pts

This criterion is linked to a learning outcome#3 – derivativeusing limits, correct algebra to justify each step

4.0 Pts

Full marks

0.0 Pts

No marks

4.0 pts

This criterion is linked to a learning outcome#3 – Tangent Line

4.0 Pts

Full marks

0.0 Pts

No marks

4.0 pts

This criterion is linked to a learning outcome#3 – GraphCurve and tangent line. Straight lines! Axes labelled and scaled.

4.0 Pts

Full marks

0.0 Pts

No marks

4.0 pts

Project Questions:

Find the limits. If an answer does not exist, write DNE. Show all applicable work, you may NOT use l’Hospital’s rule, nor derivatives. Just a number is worth 0 credit. Note that the second limit is a one-sided limit.

lim x → ∞ x − x 2 + 5 x

lim x → − 4 + | x + 4 | x + 4

Prove: lim x → 3 5 − 4 x = − 7Give both a preliminary analysis and a formal proof. (See Example 2 in Section 2.4)
Consider the function g ( t ) = t + 8
Use the definition of derivative (limits) to find the derivative of the function
Find the equation of the tangent line to the curve y = g ( t )at the point t = 1.
Graph the curve of the function and the tangent line to the curve at t = 1 on the same set of axes. (You may draw the picture by hand and upload a photo. Of course you will label and scale the axes and use a ruler. You may also use a computer to draw the graphs)

Please provide each step when solving each question, and make sure to simplify.