MAT 136 Calculus I Formulas & Explanations
1 - ANS-lim x ➡️0 sinx/x
0 - ANS-lim x➡️0 1-cosx/x
lim x➡️n- f(x) - ANS-Limit from the left
lim x➡️c+ f(x) - ANS-Limit from the right
Anything canceling on top and bottom - ANS-Holes
P>Q = No horizontal asymptotes
P=Q = Top coefficient P/bottom coefficient Q
P<Q = Horizontal Asymptote @ 0 - ANS-Horizontal Asymptotes (3)
removable discontinuity - ANS-Holes cause _____________ ____________________.
non-removable discontinuity - ANS-Vertical asymptotes cause ______-______________
____________________.
-32 (m/s^2) - ANS-Acceleration=
✖️ Inside ✖️ Derivative of the inside - ANS-Chain Rule Formula
f' (g(x)) g'(x)
Derivative of the first
F(c)= 1/(b-a) • INT<f(x)dx> - ANS-Mean Value Formula for Integrals
d/dx[integral]=fx - ANS-2nd Fundamental Theorem
b-a(f+f+f+f...) - ANS-Riemann Sum
F(b)-F(a) - ANS-Fundamental Theorem of Calculous
f">0 = Concave Up
f"<0 = Concave Down - ANS-Concavity Test
If f is continuous and differentiable on [a,b] and f(a)'=f(b)' then there is at least one point, c, such
that f'c=0 in (a,b). - ANS-Rolle's Theorem
1 - ANS-lim x ➡️0 sinx/x
0 - ANS-lim x➡️0 1-cosx/x
lim x➡️n- f(x) - ANS-Limit from the left
lim x➡️c+ f(x) - ANS-Limit from the right
Anything canceling on top and bottom - ANS-Holes
P>Q = No horizontal asymptotes
P=Q = Top coefficient P/bottom coefficient Q
P<Q = Horizontal Asymptote @ 0 - ANS-Horizontal Asymptotes (3)
removable discontinuity - ANS-Holes cause _____________ ____________________.
non-removable discontinuity - ANS-Vertical asymptotes cause ______-______________
____________________.
-32 (m/s^2) - ANS-Acceleration=
✖️ Inside ✖️ Derivative of the inside - ANS-Chain Rule Formula
f' (g(x)) g'(x)
Derivative of the first
F(c)= 1/(b-a) • INT<f(x)dx> - ANS-Mean Value Formula for Integrals
d/dx[integral]=fx - ANS-2nd Fundamental Theorem
b-a(f+f+f+f...) - ANS-Riemann Sum
F(b)-F(a) - ANS-Fundamental Theorem of Calculous
f">0 = Concave Up
f"<0 = Concave Down - ANS-Concavity Test
If f is continuous and differentiable on [a,b] and f(a)'=f(b)' then there is at least one point, c, such
that f'c=0 in (a,b). - ANS-Rolle's Theorem
