Lim x→0 (√(ax+b)-2)/x=1
You want to know the value of "a" and "b"
lim x→0 (√(ax+b)-2)/x=(√(0+b)-2)/0=(√b -2)/0;
Then if (√b -2)/0=1; the numerator must be "0"
(√b-2)=0
√b=2
(√b)²=2²
b=4
It is necessary the numerator must be "0", if the denominator is "0" and the result is equal a number.
Therefore:
lim (√(ax+4)-2)/x=1
x⇒0
I imagine you know Taylor Series.
√(ax+4)=(4(1+ax/4))¹/²=2(1+ax/4)¹/²
Remember:
(1/2)
(1+x)ᵃ=<span>Σ ( a ) x^a
</span>
In our case:
(1/2) (1/2) (1/2)
(1+ax/4)¹/²=( 0) (ax/4)⁰+( 1 ) (ax/4)¹+( 2) (ax/4)²+...
=1 +(1/2) ax/4 + -1/8 (ax/4)²+...
=1+ax/8-a²x²/128+...
Therefore:
lim (√(ax+4)-2)/x=lim [2(1+ax/8-a²x²/128+...)-2]/x=
x⇒0 x⇒0
lim [(2+ax/4-a²x²/64+...)-2]/x=
x⇒0
lim (ax/4-a²x²/64+...)/x=
x⇒0
lim x(a/4-a²x/64+...)/x=
x⇒0
lim (a/4-a²x/64+...)=(a/4-0-0-0-...)=4/a
x⇒0
Because:
lim (√(ax+4)-2)/x=1
x⇒0
Then:
4/a=1 ⇒ a=4
Answer: a=4; b=4
Answer:
It is 64
Step-by-step explanation:
Answer:
A. x >= 16/5 or x <= -3/4
Step-by-step explanation:
5x - 4 >= 12
5x > = 16
x >= 16/5
and
12x + 5 <= - 4
12x <= - 9
x <= -9/12
x <= - 3/4
Answer
x >= 16/5 or x <= -3/4
Answer: Y= -3/4x+13
Step-by-step explanation:
A line passes through the point (8,7) and has a slope of negative 3/4 Write an equation in slope-intercept form for this line.
This is what i get
Slope of a line Y= mx+b
Y= 7
X= 8
M= -3/4
7= -3/4(8)+b
7= -6+b
7+6=b
13=b
Y= -3/4x+13
Answer6x3-33x2+45x-6
Step-by-step explanation:
