If [x] denotes the greatest integer not greater than x and
F(x) = 125] [=125). 0 < x < 90. If the range of f(x) consists of k
elements then find the value of k.
Answer:
00 01 02 03 04 05 06 07 08 09
OO 1
3 04 05 06 07
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Step-by-step explanation:
If [x] denotes the greatest integer not exceeding x and if the function f defined by f(x)=
⎩
⎪
⎪
⎨
⎪
⎪
⎧
x
2
a+2cosx
btan
[x+4]
π
(x<0)
(x≥0)
is continuous at x=0, then the order pair (a, b) =
October 15, 2019
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Arthi Bhutto
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VIDEO EXPLANATION
ANSWER
Since the function is continuous at x=0,f(0
−
)=f(0
+
)
⇒
x→0
−
lim
x
2
a+2cosx
=
x→0
+
lim
b tan
[x+4]
π
For a finite limit, a has to be −2 since the numerator has to be
0 for the limit to be of the form
0
0
Using L'Hospital rule, we get
x→0
−
lim
2x
−2 sinx
=−1
⇒b tan
4
π
=−1
⇒b=−1
October 15, 2019
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The values of p and q for which the function f(x)=
⎩
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⎪
⎪
⎪
⎪
⎨
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⎧
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Step-by-step explanation:
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