Calculus 1 Exam latest update!!!
(2026-2027)|correct solution highly
graded a+
lim x→2⁻ (lnx)/(x-2) = - CORRECT ANSWERS-Since lnx approaches ln2>0, and the
denominator (x-2) approaches 0, and is negative as x→2⁻, it follows that lim x→2⁻, it
follows that lim x→2⁻ (lnx)/(x-2) = -∞
Finding vertical asymptotes on a graph: - CORRECT ANSWERS-Where ever there is a
break in the graph on the x axis.
Example: x=2 (break at 2 in the graph)
Finding horizontal asymptotes on a graph: - CORRECT ANSWERS-Where ever there is
a break in the graph on the y axis.
Example: y=3 (break at 3 on the graph)
Finding average velocity (Vav) - CORRECT ANSWERS-(b)-(a)/b-a
Finding instantaneous velocity - CORRECT ANSWERS-Plug the time into the equation
from finding the average velocity
Slope of the tangent line - CORRECT ANSWERS-m(tan)= lim h→0: [(a+h)-(a)]/h
The quotient [p(b)−p(1)]/(b-1) is the slope - CORRECT ANSWERS-of the secant line
connecting (b,p(b)) and (1,p(1))
Provided it exists, the limit lim t→1: [p(t)-p(1)]/(t-1) is the slope - CORRECT ANSWERS-
of the tangent line at the the point (1,p(1)) for p(1)
Equation of the tangent line - CORRECT ANSWERS-y=f(a)-m(x-a)
State the form of the limit, evaluate and justify
lim x→2: (x-2)/(x²-4)/4 - CORRECT ANSWERS-[(x-2)/(x-2)(x+2)]×[¼]
Definition of continuity - CORRECT ANSWERS-lim
(2026-2027)|correct solution highly
graded a+
lim x→2⁻ (lnx)/(x-2) = - CORRECT ANSWERS-Since lnx approaches ln2>0, and the
denominator (x-2) approaches 0, and is negative as x→2⁻, it follows that lim x→2⁻, it
follows that lim x→2⁻ (lnx)/(x-2) = -∞
Finding vertical asymptotes on a graph: - CORRECT ANSWERS-Where ever there is a
break in the graph on the x axis.
Example: x=2 (break at 2 in the graph)
Finding horizontal asymptotes on a graph: - CORRECT ANSWERS-Where ever there is
a break in the graph on the y axis.
Example: y=3 (break at 3 on the graph)
Finding average velocity (Vav) - CORRECT ANSWERS-(b)-(a)/b-a
Finding instantaneous velocity - CORRECT ANSWERS-Plug the time into the equation
from finding the average velocity
Slope of the tangent line - CORRECT ANSWERS-m(tan)= lim h→0: [(a+h)-(a)]/h
The quotient [p(b)−p(1)]/(b-1) is the slope - CORRECT ANSWERS-of the secant line
connecting (b,p(b)) and (1,p(1))
Provided it exists, the limit lim t→1: [p(t)-p(1)]/(t-1) is the slope - CORRECT ANSWERS-
of the tangent line at the the point (1,p(1)) for p(1)
Equation of the tangent line - CORRECT ANSWERS-y=f(a)-m(x-a)
State the form of the limit, evaluate and justify
lim x→2: (x-2)/(x²-4)/4 - CORRECT ANSWERS-[(x-2)/(x-2)(x+2)]×[¼]
Definition of continuity - CORRECT ANSWERS-lim
