Calculus 1 Exam Prep Questions with 100% Actual correct answers | verified | latest update | Graded A+ | Already Passed | Complete Solution

Calculus 1 Exam Prep
Finding Limits Numerically
lim x→c f(x) = L ⇐⇒ lim x→c^- f(x) = L and lim x→c^+ f(x) = L




Theorem 1.2.1-1.2.2: Finding Limits Algebraically
lim x→c f(x) = f(c)




Brainpower
Read More
Theorem 1.2.3: Limits of Transcendental Functions
Let a and c be real numbers with a > 0 and a ≠ 1. The rules apply to the following below as
long as it is defined at c.

lim x→c sinx = sinc
lim x→c cosx = cosc
lim x→c tanx = tanc
lim x→c cscx = cscc
lim x→c secx = secc lim x→c cotx = cotc lim x→c ax = ac
lim x→c loga x = loga c




Absolute
|x| = { x, x>=0
|x| = { -x, x<0




Theorem 1.2.4: Eliminating Zero Denominators Algebraically
lim x→c f(x) = lim x→c g(x)




Theorem 1.2.6: Squeeze Theorem
g(x) ≤ f(x) ≤ h(x)




Theorem 1.2.7: Squeeze Theorem with Sine
lim θ→0 sinθ/θ= 1

, (use radians)




Theorem 1.2.8: Squeeze Theorem with Cosine
lim θ→0 cosθ−1/θ = 0
(use radians)




Theorem 1.4.4: Limits Involving Infinity with Linear Functions
lim x→−∞ (mx + b) =(−∞, m > 0
∞, m < 0

lim x→∞ (mx + b) =(∞, m > 0 −∞, m < 0




Theorem 1.4.5: Limits Involving Infinity with Power Functions
lim x→ ∞ x^r = ∞
Let r be a positive real number.




Theorem 1.4.6: Limits Involving Infinity with Power Functions
lim x→ -∞ x^r = { -∞, q= 1, 3, 5...

lim x→ -∞ x^r = { undef, q= 2, 4, 6...

Let r = p/q in a reduced form




Theorem 1.4.9: Limits Involving Infinity with Fraction and Power Functions
lim x→∞ 1/x^r = 0

lim x→-∞ 1/x^r = { 0, q= 1,3, 5...

lim x→-∞ 1/x^r = { undef, q= 2, 4, 5...

Let r = p/q in a reduced form




Theorem 1.4.11: Limits Involving Infinity with Polynomial Function
lim x→−∞
p(x) = lim x→−∞
anxn ={