MCV4U ~ All things Limits and
Derivatives study set correctly solved
2026/2027
Limits [Definition and Conditions] - correct answer ✔What the value of a function appears to equal as
x approaches a certain value (c)
For a limit to exist, the left and right hand limit must both exist and be equal.
Limits: Sandwich Theorem - correct answer ✔If a function (f) is sandwiched between two functions
and the limit of both functions are equal (both equal to L) when they approach c, then the limit of the
function (f) also equals (L)
Limits: Asymptotes - correct answer ✔Vertical Asymptote:
When the left or right hand limit of a function approaching a value (c) equals ±∞
Note: If left and right hand approaches the same infinity (both to negative ∞), write that the limit
approaches -∞ rather than DNE.
For rational functions, there is a vertical asymptote for when the denominator equals zero.
End Behaviour
Polynomial Function: Behaves at infinity as the leading term ~
Horitzontal Asymptote: When the limit of a function as x → ∞ = b, then y=b is the horizontal aymptote.
For rational functions, the end behaviour is determined using the end behaviour of the numerator and
denominator [assuming num. and den. are polynomials]
Derivatives study set correctly solved
2026/2027
Limits [Definition and Conditions] - correct answer ✔What the value of a function appears to equal as
x approaches a certain value (c)
For a limit to exist, the left and right hand limit must both exist and be equal.
Limits: Sandwich Theorem - correct answer ✔If a function (f) is sandwiched between two functions
and the limit of both functions are equal (both equal to L) when they approach c, then the limit of the
function (f) also equals (L)
Limits: Asymptotes - correct answer ✔Vertical Asymptote:
When the left or right hand limit of a function approaching a value (c) equals ±∞
Note: If left and right hand approaches the same infinity (both to negative ∞), write that the limit
approaches -∞ rather than DNE.
For rational functions, there is a vertical asymptote for when the denominator equals zero.
End Behaviour
Polynomial Function: Behaves at infinity as the leading term ~
Horitzontal Asymptote: When the limit of a function as x → ∞ = b, then y=b is the horizontal aymptote.
For rational functions, the end behaviour is determined using the end behaviour of the numerator and
denominator [assuming num. and den. are polynomials]
