MATH 1041- Midterm Exam Guide - Comprehensive Notes for the exam ( 30 pages long!)

• School: Temple University
• Department: Mathematics
• Course: MATH 1041
• Professor: farhanabedin

Document Summary

The word tangent is derived from the latin word tangens, whi(cid:272)h (cid:373)ea(cid:374)s (cid:862)tou(cid:272)hi(cid:374)g. (cid:863) thus, a tangent to a curve is a line that touches the curve. In other words, a tangent line should have the same direction as the curve at the point of contact. Example 1 find an equation of the tangent line to the parabola (cid:1877)= (cid:1876)(cid:2870) at the point (cid:1842)(cid:4666)(cid:883),(cid:883)(cid:4667). We will be able to find an equation of the tangent line (cid:1872) as soon as we know its slope (cid:1865). But observe that we can compute an approximation to cuts (intersects) a curve more than once] We choose (cid:1876) (cid:883) so that (cid:1843) (cid:1842). For instance, for the point (cid:1843)(cid:4666)(cid:883). (cid:887),(cid:884). (cid:884)(cid:887)(cid:4667) we have (cid:883). (cid:887) (cid:883) = (cid:883). (cid:884)(cid:887)(cid:882). (cid:887)=(cid:884). (cid:887) (cid:1865)(cid:3017)(cid:3018)= (cid:884). (cid:884)(cid:887) (cid:883) The tables (figure 2) show the value of (cid:1865)(cid:3017)(cid:3018)for several values of (cid:1876) close to 1.