11-13-2010, 03:53 PM
Idea solution check it out.
Q1. Use epsilon-delta definition to prove
Limit as x-->-3 (x^2-9)/(x+3)= -6
Ans. |x+3|<epsilon iff 0<|x+3|<delta
Q2. Find the points of discontinuity of the given function
f(x)=(x+3)/|x^2+3x|
Ans. Points of discontinuity are 0 and -3 in both the cases (when absolute sign is removed we get two cases. 1. (x^2+3x) and 2. -(x^2+3x) .. am I right??)
Q3. Find a non-zero value for the constant “k” so that
f(x)= tan(kx)/x if x<0
3x+2k^2 if x>0
will be continuous at x=0
Ans. k=1/2
Note: Please donot consider this answers 100% true as there may be some mistake from my side (I'm not a cheetah in math
) ... anyways .. please if you find your answers different from mine .. Kindly do notify so we can discuss which answer are correct. Thank you!!
Q1. Use epsilon-delta definition to prove
Limit as x-->-3 (x^2-9)/(x+3)= -6
Ans. |x+3|<epsilon iff 0<|x+3|<delta
Q2. Find the points of discontinuity of the given function
f(x)=(x+3)/|x^2+3x|
Ans. Points of discontinuity are 0 and -3 in both the cases (when absolute sign is removed we get two cases. 1. (x^2+3x) and 2. -(x^2+3x) .. am I right??)
Q3. Find a non-zero value for the constant “k” so that
f(x)= tan(kx)/x if x<0
3x+2k^2 if x>0
will be continuous at x=0
Ans. k=1/2
Note: Please donot consider this answers 100% true as there may be some mistake from my side (I'm not a cheetah in math
) ... anyways .. please if you find your answers different from mine .. Kindly do notify so we can discuss which answer are correct. Thank you!!