Q: Calculate each of the limits in Exercises
A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…
Q: (2x-1)(3-x)
is
(x-1)(x+3)
limx→0
A: Given problem is :
Q: Compute
x-+xX
lim
X-700
It Ttx
Sinx
2) Lim
X-70
CUSX-1
X3-1
1L-X
A: Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: Compute limx→∞ 4x^3+6x−2 / 3x^3−2x^2+x+1
A:
Q: Find lim(2 – x)tan(r2/2)
A:
Q: 9x +1
lim
x - 1
V1+x-1
lim
x-0
lim
2x2 + 3x
lim
x05x2 - 2x
Dr ohammed Jas
A:
Q: 1) lim (2x – 3) = 1
x-2
2) lim|x| = 0
x²-9
3) lim
х-з х-3
9 3
A: 1)limx→2(2x-3)=1read : limit x tends to 2, (2x-3) is 1proof:limx→2(2x-3)=2(2)-3
Q: х2 +x — 2
Vx + 4 – 2
-
-
(а) lim
x→-2
(b) lim
x + 2
y
y
2
1.00
1
0.75
0.50
-3 -2 - 1
1 2 3
-3
-4 -3…
A: (a)limx→-2x2+x-2x+2blimx→0x+4-2x
Q: 2) IF f(x) = {"
(x + 2 , – 1<x<0
x, 0<x< 1
find limf(x)
%3D
A: To find lim(x tends to inf) f(x)
Q: 10
Find
lim x12s
3.
X->-
X -25
2 lim
Jx +3 - 2
メ→」
O lim Sitx - -x
3.
1-X
2 X
A:
Q: find:
a) Lim x4-1
x2
b). Lim
10x-3 SinX
A: We have to find the following limit
alimx→1x4-1x2-1
blimx→010x-3sinxx
Q: B. Find the limit.
Зх— 1
5. lim
х-1/3 9х2-1
x3- 1
6. lim
х+1 х-1
Vx+5 -2
7. lim
X→-1
х+1
Vx-1
4. lim…
A:
Q: Find the limits
A: Given Data
The limit is limx→-32-x2-5x+3.
Solve the given limit expression,…
Q: Compute
1) Lim
X-3.9טTX
2) um
X-71T
sin x
TT-X
3) um
-X.
X2-X-6
A: (1) The given expression of limit is
Q: Show that
4z2
z2 +1
1
(b) lim-
z→1(z – 1)3
(a) lim
: 43B
= 00;
(c) lim
= 00.
-
-
z(I – 2) 0+2
I- 2…
A: We will use the simple calculations using some usual formulae to evaluate these limits.
Q: Find Lim-0.0 (r² + y²) In(x² +y²)
'(xy)(0,0)
A:
Q: : limx->0(1/x3)
A: We have to simplify the given expression.
The given expression is limx→01x3∫0xt2t4+1dt
Q: Prove the limit statements
A: Given: fx=4-2x,x<16x-4,x≥1
we know that limit of any given function at given point exist only if…
Q: (a)
lim
x→2 arctan(7-3x)-"
2х-4
4
(b)
10-e5x
lim
x→00 16-x2
A: See the calculation and explanation below
Q: Find the limits
A: To evaluate the limit: lim1x2-4
(a). When x→2+.
Evaluating the limit.
limx→2+1x2-4=12+2-4=10+=∞…
Q: ® Find Lim
X->2
x¥ _ 2x² - 8
x² - 4
(2
,X +2
Lim 3X
X→3
X- 3
-3
X+3
O Lim
© Lim t- fo
-) ,X EO
X+2
2
A: "Since you have posted a question with multiple sub-parts, we will solve first three subparts for…
Q: if
fn(x) – f(x)|dx = 0
lim
show
1
|fn(x) – f(x)|
|1+ fn(x)f(x)|
lim
dx = 0
A: In the given question w have to prove that if the integration
limn→∞∫01fn(x)-f(x)dx=0then…
Q: By L'Hopital's Rule,
X-2
lim
x→2 X²-1
1 1
lim. =
x→2 2X 4
A: L’Hospital’s Rule:
Suppose that limx→a f(x)g(x)=00 OR limx→a f(x)g(x)=±∞±∞
where a can be any…
Q: Q.1: Evaluate
Vx+25 -5
х2-10х
(1) lim
(2) lim
x-12 Vx+4
x (х+3)
2x2+3
x2-25
(3) lim
(4) lim
X-5 x-5…
A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…
Q: Find the Limit:
1. lim (2x + 5)
x--7
3. lim(-x + 5x 2)
5. lim 8(t - 5)(t - 7)
A:
Q: 1
Lim
x→0*
x0x
1
sin x
A:
Q: S 1.4x + 0.8,
x -2
f(-2) =
lim f(x) =
x--2-
lim f(x) =
x--2+
lim f(x) =
||
x--2
A: E
Q: 5. lim V2x +1
X-4
6. lim -)
ズー1
x-1
CABA
3x+4 if x <-3
AT
7. lim f(x), where f(x) =
2-4 ifx2-3
A:
Q: 13. lim f(x), where
Sx+2 xS2
3x-5 x> 2
f(x) =
14. lim f(x), where
Sx* - x +1 x 3
A:
Q: Find the limit.
y
6-
5-
4
3-
2
1-
3-2 -1
-1
1\2
3
4 5
-2t
limz-0 f (x)
A:
Q: Find
lim
1-CoS 3X
Xう。
tan x -1
lim
メー X -
X->
A: Solution is given below..
Q: Estimate the limit numerically for lim
X4 x²-3x-4
4
3.9
3.99
3.999
4.001
4.01
4.1
X.
x - 4
Lx2 - 3x…
A:
Q: 1
lim
- 1)dt
x→1|1
[1 – x
A: We have to find the limit of the complex expression involving integration . first we have to find…
Q: 5. lim (ex – V2x)
x→0+
A:
Q: -11x
lim
I+00 11 + 2x
-1
6x – 12
lim
1-00 r3 + 9x – 14
,2
lim
x→0 12 – 15x?
V2² + 15x
lim
5х — 13…
A:
Q: 1x+21
Ex.2: lim
ダー→ -2
(x+3)
x+2
A: limx→-2-(x+3)|x+2|x+2
Q: 3
limy 0
1 -
x!
A: This is the problem of limit and calculus.
Q: 1.
lim f(x) where flx) = (-3x + 8 if x -2
A: Use limit condition.
Q: (1) lim
t2
(2) lim
x0 Vx2 +3
2x + 1
-1
x00 7 - t2
x2
1
(4) lim
3t2
n2
(6) lim
x0 Vn3 + 2n
5t
(3) lim…
A:
Q: GIVEN :
2x
2х
- 2x ) +
6
1
1
f (x) = 1
--x
8
g(x) = 3(x +
+ 4 h(x) =
6
-
||
3
a.lim -4 · f (x)
d.lim…
A: For (a),
limx→2-4 f(x)=limx→ 2-41-18xPlug in the value x=2=-41-18· 2=-3
Q: 9 – y².
|-(16 * 10)x – (4 * 10)
lim .
-] + lim
y--33 + y
x + 10
x--10
A: Given, limy→-39 - y23 + y + limx→-10-16*10x-4*10x + 10
Q: 2. Compute
lim x" (1 + x)* – e).
1/x
x→0
A:
Q: x²+x5-2y
lim
(xy)-(3,9)
%3D
x-
A: Given limit
lim(x,y)→(3,9)x2+xy-2yx-y
Q: Q2) Find :
(a) lim (2 + x)
x-4+
16-x
1-secx
0 sinx
cos2x
sintx
(b) lim
(c) lim
(d) lim
x-0 sin2x…
A: Dear student,
According to bartleby guidelines when student post more than one question then expert…
Q: 1/x
2
In(5x) H
lim
2 5x
= lim
lim
lim
X- V 5x
5x
2
5x
A: The solution of given problem as follows:
Q: х —
1
lim
x→1+
Vx + 2
A: Here we need to find the right hand limit only.To find the required limit substitute the variable…
Q: -2x - 4
f)
lim
x--2 x + 2x
ut
|
g)
lim
u-1 u3
1
4х — х2
h)
lim
x-4 2 - Vx
Ya
A: As per our guideline we are supposed to answer only first three subparts. Kindly repost other parts.…