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71. Examine the following functions for continuity :

straight f left parenthesis straight x right parenthesis equals fraction numerator 1 over denominator straight x minus 5 end fraction

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72. Examine the following functions for continuity :

straight f left parenthesis straight x right parenthesis equals fraction numerator straight x squared minus 25 over denominator straight x minus 5 end fraction

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73. Examine the following functions for continuity :

f(x) = | x – 5 |

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74. Discuss the continuity of sine function

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75. Prove that the function defined by f(x) = tan x is a continuous function

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76. Discuss the continuity of the cosine, cosecant, secant and cotangent functions.

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77. Discuss the continuity of the following functions :
(a) f(x) = sin x + cos x

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78. Discuss the continuity of the following functions :
–f(x) = sin x – cos x

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79. Discuss the continuity of the following functions :
f(x) = sin x.cos x

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80. Let f be a function such that f(x + y) =f(x) +f(y), x,y∈ R
Show that if f is continuous at x = 0, then it is continuous everywhere.

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