A Function is defined to be rule that associates to may given number x a single number f(x) to be read as function of x. f(x) does not mean f time x. It means given x, the rule f results the number f(x).
Symbolically it may be written in the form y=f(x).
Results
#1. If f(x)=x²-5 evaluate f(3),f(-4),f(5) and f(1)
If f(x)=x²-5 evaluate f(3),f(-4),f(5) and f(1)
f(x)=x²-5
f(3)=3²-5 = 9-5=4
F(-4)=(-4)² -5 =16 -5 =11
F(5)=5²-5=25-5=20
F(1)=1² -5 =1-5 =-4
#2. If f(x)=1-x/1+x then f(f(1/x)) is equal to
If f(x)=1-x/1 x then f(f(1/x)) is equal to
f (1 1-x/1 x)/(1-1-x/1 x)
– 2/2x
-1/x
#3. If g(x) =3 -x² then g(x) is
If g(x) =3 -x² then g(x) is
Answer : An even Function
#4. The value of the limit when n tends to infinity of the expression (7n^3- 8n^2+10n-7)/ (8n^3-9n^2+5) is
The value of the limit when n tends to infinity of the expression (7n^3- 8n^2 10n-7)/ (8n^3-9n^2 5) is
(7*3*2)/(8*3*2)
42/48
answer = 7/8
#5. lim x→∞ [4/x^3+2]
lim x→∞ [4/x^3 2]
lim x→∞(1 1/x)x=e
SO x^3
e=3
#6. The value of the limit of f(x) as x →2 f(x)=e ͯ ³+ 3 ͯ ² +2 ͯ +1
The value of the limit of f(x) as x →2 f(x)=e ͯ ³ 3 ͯ ² 2 ͯ 1
put 2 in x
e^2^3 3^2^2 2^2 1
e^ 8 12 4 1
e ^25
#7. lim x→0 4x+2x-1/x
lim x→0 4x 2x-1/x
a˟-1/x=Logₑ a
Logₑ 4*2
Logₑ 8
#8. lim x →3 = x²-9/x-3
lim x →3 = x²-9/x-3
x²-(3)²/x-3 = na^(n-1)
2(3)^(2-1)
6
#9. lim x →2 2x²-7x +6/5x²-11x+2 is equal to
lim x →2 2x²-7x 6/5x²-11x 2 is equal to
(2x-3)(x-1)/(5x-1)(x-2)…….put x→2
1/9
#10. If f(x) =2x²+6x-5/12x²+x-20 is to be discontinuous then
If f(x) =2x² 6x-5/12x² x-20 is to be discontinuous then
answer x= 5/4
#11. lim x→0 log (1+7*x/3)/x
lim x→0 log (1 7*x/3)/x
lim x→0 log(1 x)/x=1
log (1 7x/3)/7x/3*3/7
log 7/3
#12. lim x→0 (1+5x)^1/x
lim x→0 (1 5x)^1/x
By rule lim x→0 (1 x)^1/x=e
(1 5x)^1/5x*5
e^5
#13. The value of the limit when x tends to zero of the expression (1+n)^1/n is
(1 n)^1/n is
By rule lim tends to x is 0 (1 x)^1/x÷x = e
Answer= e
#14. Evaluate lim x tends to 2 x²+2x-1/√x²+2
lim x-> 2 x² 2x-1/√x² 2
lim x-> 2 (x² 2x-1)/lim x-> 2√x² 2
lim x-> 2 x² lim x-> 2x-1/lim x-> 2√x² 2
(2)² 2*2-1/√(2)² 2
7/√6
#15. lim x→0 x/log(1+x) is equal to
lim x→0 x/log(1 x) is equal to
By Limit rule
Answer is 1
#16. Lim x→0 (x+6/x+1)^x+4
Lim x→0 (x 6/x 1)^x 4
By using Limit rule
=limx→0(1 5x 1)(x 4)
limx→0(1 5)^x
e^5
#17. 3x^2 + 2x -1 is continuous
3x^2 2x -1 is continuous
Answer At x=2 & For every value of x
#18. Lim x->2 (x^2-5/x-4)
Lim x->2 (x^2-5/x-4)
2(2)^2-5/2-4
8-5/-2
=-3/4
#19. lim n-> 2 x^5-32/x-2
lim n->2 x^5-32/x-2
lim n->2 x^5 -(2)^5/x-2
5(2)^(5-1)
5*16
=80
#20. Lim x→0 sin(5x/x)
Lim x→0 sin(5x/x)
Lim x→0 sin(5x)/5x*1/x)
1/¹/₅
5