Definition
What is limit in calculus?
A limit tells us the value that a function approaches as that function's inputs get closer and closer to some number.
What is substitution?
is a method of determining limits where the value that x is approaching is substituted into the function and the result is evaluated
What is finding limit by factoring?
By canceling out common factors
What is L 'Hospital's Rule?
It says that the limit when we divide one function by another is the same after we take the derivative of each function
limx→2(8−3x+12x2)
50
In the 19th century, Augustin-Louis Cauchy, Karl Weierstrass, and Bernhard Riemann reformulated calculus in terms of limits, rather than infinitesimals.
When can you use direct substitution for limit?
when you have a simple functions with additions, subtractions, divisions, multiplications, powers and roots
How do you use the factorization formula?
What is L 'Hospital's Formula?
lim x->c f(x) / g(x) = lim x->c f'(x) / g'(x)
lim x->-3 (6+4t) / (t^2+1)
-3/5
What is the basic concept of limits?
Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals
lim x->3 (x^2 - 4) / (x - 2)
5
(a + b)^2 = ?
a^2 + 2ab + b^2
How to apply L 'Hospital's Rule?
lim h->0 [(6+h)^2 - 36] / h
12
What are three ways to solve limits?
substitution, factoring, and the conjugate method.
lim x->4 [3(x - 1)] / (x + 4)
9/8
(a - b)^3 = ?
a^3 - 3a^2b + 3ab^2 - b^3
lim x->2 (x^3 - 7x^2 + 10x) / (x^2 + x - 6)
-6/5
lim x->-5 (x^2 - 25) / (x^2 + 2x - 15)
5/4
How are limits useful in daily life?
It helps to measure the strength of the magnetic field, electric field, etc. Limits are used to figure out the most relevant pieces of information from the large complex functions.
lim x->5 (5x)^1/2 - 12
-7
(a + b + c)^2 = ?
a^2 + b^2 + c^2 + 2ab + 2bc + 2ca
lim x->∞ [ln(3x)] / x^2
0
lim x->4 (x^1/2 - 2) / (x - 4)
1/4