Consider the function f(x)=(ax+1bx+2)x, where a2+b2≠0 then limx→∞f(x)
A
exists for all values of a and b
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
is zero for 0<a<b
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
is non existent for a>b>0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
is e−(1a) or e−(1b) if a=b
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct options are B is zero for 0<a<b C is non existent for a>b>0 D is e−(1a) or e−(1b) if a=b Case 1. 0<a<b limx→∞f(x)=limx→∞(ax+1bx+2)x=limx→∞(a+1/xb+2/x)x=limx→∞(ab)x=0 Case 2. a>b>0 limx→∞f(x)=limx→∞(ax+1bx+2)x=limx→∞(a+1/xb+2/x)x=limx→∞(ab)x=∞ Case 3. a=b form of the limit is 1∞ limx→∞f(x)=limx→∞(ax+1ax+2)x=elimx→∞(ax+1ax+2−1)x=elimx→∞(−xax+2)=e(−1a)