Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

131. Prove that the greatest integer function [x] is not differentiable at x = 1.

79 Views

132. Prove that the function f given by f(x) = |x - 1 |, x ∈ R is not differentiable at x = 1.

110 Views

133.

Prove space that space straight f left parenthesis straight x right parenthesis equals open vertical bar straight x minus 3 close vertical bar space has space no space derivative space at space straight x equals 3.

78 Views

Here space If space straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell straight x space sin 1 over straight x comma space space space straight x not equal to 0 end cell row cell 0 space space space space space space space space space comma space space space straight x equals 0 end cell end table close straight R. straight H. straight D equals Lt with straight x rightwards arrow 0 to the power of plus below fraction numerator straight f left parenthesis straight x right parenthesis minus straight f left parenthesis 0 right parenthesis over denominator straight x minus 0 end fraction equals Lt with straight x rightwards arrow 0 to the power of plus below fraction numerator straight x space sin begin display style 1 over straight x end style minus 0 over denominator straight x end fraction equals Lt with straight x rightwards arrow 0 to the power of plus below sin 1 over straight x comma space which space does space not space exist therefore space straight f space is space not space differentiable space at space straight x equals 0

78 Views

135.

Syntax error from line 1 column 169 to line 1 column 176.

78 Views

136. Examine the derivability of the following functions :
|x| at x = 0

90 Views

137. Examine the derivability of the following functions :
|x²| at x = 0

80 Views

138. A function f is defined as

straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 1 plus straight x comma space if space straight x less or equal than 2 end cell row cell 5 minus straight x comma space if space straight x greater than 2 end cell end table close

Show that f is not differentiable at x = 2.

78 Views

139. Examine the derivability of the following function:

straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell straight x squared space sin 1 over straight x comma space straight x not equal to 0 end cell row cell space space space space space space space 0 space space space comma space space space space straight x equals 0 end cell end table close

73 Views

140. Examine the derivability of the following function:

straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell 3 minus 2 straight x comma space straight x less than 2 end cell row cell 3 straight x minus 7 comma space straight x greater or equal than 2 end cell end table close at space straight x equals 2

72 Views