Limits
Product, Quotient, Chain Rule
Rolles Theorem
&
Mean Value Theorem
Anti-derivative
Logs & ln
100
Lim x ²+x+2/x+1 as x->7
58/8 or 7.25
100
4(x³+3)²
8(x³+3)¹(3x²)
100
f(x)= x²-3x+2 [1,2] ROLLES THEOREM
3/2
100
4x√(x²-5) dx
4(x²-5)/2(2x) +C
100
log(base5)x
1/ (ln5)(x)
200
lim x ²-9/x+3 as x->4
1
200
3x²/ x^4+7x
(x^4+7x)(6x)-(3x²)(4x³+7)/ (x^4+7x)²
200
f(x)= x^4-2x² [-2,2] ROLLES THEOREM
0, 1, -1
200
8x²(3-x³)^4
8(3-x³)^5/ 5(-3) +C
200
log(base7) 3x²+2
6x/ (ln7)(3x²+2)
300
f(x)= 6/x ²-4x+3 *lim x->3- * *lim x->3+* * lim x->3*
lim x->3- = -∞ lim x->3+ = +∞ lim x->3 =DNE
300
√(4x²-1)
8x/2√(4x²-1)
300
f(x)= x³-x²-2x [-1,1] MEAN VALUE THEOREM
-1/3 , 1
300
(3sec²3x)(tan3x)²
(tan3x)³/3 +C
300
ln2x
1/x
400
lim 4x³+3x-5/7(x-3)² as x->∞
∞
400
(6x²)(4x³-12x²+9x)
(6x²)(12x²-24x+9)+(12x)(4x³-12x²+9x)
400
f(x)= x²-3x+2 [1,2] ROLLES THEOREM
3/2
400
7xsin3x²
7(-cos3x)²/12 +C
400
ln(4x²-3x)
8x-3/4x²-3x
500
lim x/ √(x+1) -1 as x->0
2
500
(14x²-9x)/ (11x³+8x²-17x)
(11x³+8x²-17x)(28x-9)-(14x²-9x)(33x²+16x-17)/ (11x³+8x²-17x)²
500
f(x)= x²-3x+2 [0,2] ROLLES THEOREM
DOES NOT MATCH SO.. DOES NOT EXIST
500
4sec²7x
4tan7x/7 +C
500
log(base 6) [(3x+4)/x^5)]
3/ (ln6)(3x+4) - 5[1/x]
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