Thread: Need help with some Ln and base e functions

1) Find the equation of the tangent to the curve y = e^-x at the point where x = -1.

for this i found the slope of the tangent to curve at x = -1 to be -e (not sure if this is correct) and i dunno what to do after that


2) Find the equation of the tangent to the curve y = 2 - e^-x at the point where x = 1.
for this i found the slope of the tangent to curve at x = 1 to be 1/e (not sure if this is correct) and i dunno what to do after that


3) Find the equation of the tangent to the curve y = ln 2x at the point where x = e/2.
for this i found the slope of the tangent to curve at x = 1 to be 1/2e (not sure if this is correct) and i dunno what to do after that


Thanks in advance

1) Find the equation of the tangent to the curve y = e^-x at the point where x = -1.

for this i found the slope of the tangent to curve at x = -1 to be -e (not sure if this is correct) and i dunno what to do after that

after that use y - y1 = m(x - x1) to het
y - e = -e(x + 1)
y = -ex


parts 2 and 3 to come soon

2) Find the equation of the tangent to the curve y = 2 - e^-x at the point where x = 1.
for this i found the slope of the tangent to curve at x = 1 to be 1/e (not sure if this is correct) and i dunno what to do after that

y - 2 + 1/e = x/e - 1/e
y = (x + 2)/e +2




3) Find the equation of the tangent to the curve y = ln 2x at the point where x = e/2.
for this i found the slope of the tangent to curve at x = 1 to be 1/2e (not sure if this is correct) and i dunno what to do after that

gradient at x is actually 1/x so at x it is 2/e

same again

y - 1 = 2x/e - 1
y = 2x/e

hope that helps you