# Limits

This set of MATLAB test focuses on “Limits”.

1. What will be the output of the following code?

syms x;limit('(sin(x)/x)',x,Inf,'left')

a) 0
b) Nan
c) Inf
d) 1

2. What will be the output of the following code?

sym x; limit(ans^2\sin(ans),Inf)

a) 0
b) Error
c) Nan
d) Cannot be determined

3. The condition for removal discontinuity is ____________
a) Left hand limit = right hand limit ≠ function value
b) Left hand limit ≠ right hand limit = function value
c) Right hand limit ≠ left hand limit = function value
d) Left hand limit ≠ right hand limit ≠ function value

4. Can we perform infinite series summation in MATLAB?
a) Yes
b) No
c) Cannot be determined
d) Sometimes

5. Negative limiting values cannot be applied to logarithmic functions in MATLAB.
a) True
b) False

6. The result of the following code?

syms x;limit(sin(x)/x,Inf,’right’)

a) Error due to symbolic argument
b) Error due to direction of approach of limiting value
c) 1
d) 0

7. To do double limits, we can use __________
a) limit(limit())
b) limit( multiple inputs)
c) cannot be done in MATLAB
d) lim()

8. What is the output of the following code?

syms x y;limit(y*x,1,x,'left','left')

a) Error
b) Error due to symbolic argument y
c) Error due to multiple inputs
d) y

9. What is the output of the following code?

syms n;limit((1+1/n)^n,Inf,’right’)

a) Nan
b) Inf
c) Error
d) e(1)

10. We cannot calculate continuity at infinity in MATLAB.
a) True
b) False

11. Can we check the continuity of a function in MATLAB?
a) Yes
b) No
c) Sometimes
d) Rarely

12. What is the output of the following code?

limit(x^2,x,1,’left’)

a) 1
b) 0
c) x should be declared symbolic
d) Cannot be determined

13. What is the error in the following code?

limit(x^2,y,1,'left')

a) The function
b) The symbolic argument
c) Left should’ve been without
d) No error

14. How can we check whether the limn→3+ n-1 exists?
a) limit(n-1,n,3)
b) syms n;limit(n-1,n,3,’right’)
c) syms n;limit(n-1,3,’right’)
d) syms n;limit(n-1,3,n,’right’)

15. What is the output of the following code?

syms n;limit(n-1,n,Inf,’right’)

a) Inf
b) Nan
c) 0
d) Error

16. What is the output of the following code?

syms n;limit(n-1,n,nan,'left')

a) 0
b) Inf
c) Nan
d) Error

17. What is the output of the following code?

syms x;limit(((1-cos(x))/(x^2)),x,0)

a) 0
b) 12
c) Error
d) Infinite

18. What is the output of the following code?

syms x;limit(((1-cos(x))/(x^2)),x,Inf)

a) Inf
b) 0
c) Nan
d) Error

19. What is the output of the following code?

syms x;limit((((Inf*x)-cos(x))/(x^2)),x,0)

a) limit(Inf/x, x, 0)
b) Inf
c) Nan
d) Error

20. What is the output of the following code?

limit(0/0, x, 0)

a) Nan
b) Inf
c) 0
d) Error

21. If a function is differentiable, the function is continuous.
a) True
b) False

22. What is the code to solve limx→1(logx)logx?
a) syms x;limit(‘log(x)^(log(x))’,x,1)
b) limit(‘log(x)^(log(x))’,x,1)
c) syms x;limit(log(x)^(log(x)),x,1)
d) Cannot be solved

23. What is the output of the following code?

sym x;limit(log(x)^(log(x)),x,1)

a) Error
b) 1
c) 0
d) Cannot be defined

24. What is the output in the following case?

syms x; limit(sin(x)/x)

a) 0
b) 1
c) Error
d) garbage value

25. What will be the output of the following code?

sym x;limit(‘log(x)^(log(x))’,1,’right’)

a) Error
b) 0
c) 1
d) Nan