Consider where [.] represents the greatest integer function. If f(x) is continuous at x=0, then is equal to
1
2
0
-1
For x=0 and x=0+h ;[x+3]=3
For left hand limit to exist, we must have a+3=0
For continuity, we have
Let , then x{x} ({⋅} denotes fractional part of x) is equal to
1
None of these
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If stands for the sum of given series
where n is an even positive integer, is
0
We have
Therefore the value of given expression
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The set of points where the function is differentiable is
R
Since |x-1| is not differentiable at x=1. So. is not differentiable at x=1. Hence, the requried set is R-|1|.
View Full Answer(1)A steel rod of length 400 cm is clamped at the middle. The frequency of the fundamental mode for the longitudinal vibrations of the rod is 2.5K Hz . Find the speed of sound in steel.
20km/s
25km/s
15km/s
26km/s
distance between two connected antinode
frequency of fundamental mode is
View Full Answer(1)In the expansion of the coefficient of is
210
310
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Locus of the midpoint of any focal chord of is
Let the midpoint be . Equation of this chord is . i.e., . It must pass through
. Thus required locus is
Hence option 2 is correct.
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If at t=0, a travelling wave pulse on a string is described by the function . What will be the wave function representing the pulse at time t, if the pulse is propagating along positive x-axis with speed 4m/s?
If v is the speed of the wave, then
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