MEMORIAL UNIVERSITY OF NEWFOUNDLAND
DEPARTMENT OF MATHEMATICS AND STATISTICS
MATHEMATICS 1000
Assignment 7
Fall 2020
Due: Friday, November 13th, 2020 at 11:59pm. SHOW ALL WORK. See the
Gradescope Handout for submission information.
Note: You should complete the WebAssign problem sets “Implicit Differentiation”
and “Derivatives of Logarithmic Functions” before you work on this assignment.
1. The curve defined by the equation
3(x2 + y 2 )2 = 100xy
is known as a lemniscate. (Its graph is shown in Figure 1.) Find the equation of the tangent
line to the lemniscate at the point (1, 3).
3
2
1
y
0
–1
–2
–3
–3
–2
–1
0
1
2
3
x
Figure 1: The graph of the equation 3(x2 + y 2 )2 = 100xy.
2. Use logarithmic differentiation to find the derivative of
x7 e x
√
y=
.
tan(x) x2 + 5