Notes On Concept of Infinity - CBSE Class 12 Maths
The nature of the function f(x) = $\frac{\text{1}}{\text{x}}$ = $\underset{x\to {\text{0}}^{\text{+}}}{\text{lim}}\frac{\text{1}}{\text{x}}$     x   1   0.5   0.2   0.1=10-1   0.01=10-2   …   10-n   f(x)   1   2   5   10 = 101   100 = =102   …   10n ⇒ For a positive real number very close to 0, the value of the function will be a large number. = $\underset{x\to {\text{0}}^{\text{+}}}{\text{lim}}\frac{\text{1}}{\text{x}}$ = + ∞ ⇒ Right hand limit of f(x) at 0 does not exist. = $\underset{x\to {\text{0}}^{\text{–}}}{\text{lim}}\frac{\text{1}}{\text{x}}$   x   - 1   - 0.5   - 0.2   -10-1   10-2   …   -10-n   f(x)   - 1   - 2   - 5   -101   -102   …   -10n ⇒ For a negative real number very close to 0, the value of the function will be a very small number. = $\underset{x\to {\text{0}}^{\text{+}}}{\text{lim}}\frac{\text{1}}{\text{x}}$ = – ∞ ⇒ Left hand limit of f(x) at 0 does not exist. The nature of the function f(x) = tan x   xo   tan xo   0°   0   45°   1.0000   60°   1.7320   85°   11.4300   89°   57.2899   89.9°   572.9572   89.99°   5729.5778   89.999°   57295.7795   89.9999°   572957.7951   90°   Infinity ⇒ For an angle very close to 90° from the left side, the value of the function will be a large number. This number is represented by + ∞. = = + ∞   xo   tan xo   180°       0   150°   - 0.5773   120°   - 1.7320   100°   - 5.6712   91°   - 57.2899   90.1°   - 572.9572   90.01°   - 5729.5778   90.001°   - 57295.7795   90.0001°   - 572957.7951   90°   Infinity ⇒ For an angle very close to 90° from the right side, the value of the function will be a small number. This number is represented by – ∞. = = – ∞

#### Summary

The nature of the function f(x) = $\frac{\text{1}}{\text{x}}$ = $\underset{x\to {\text{0}}^{\text{+}}}{\text{lim}}\frac{\text{1}}{\text{x}}$     x   1   0.5   0.2   0.1=10-1   0.01=10-2   …   10-n   f(x)   1   2   5   10 = 101   100 = =102   …   10n ⇒ For a positive real number very close to 0, the value of the function will be a large number. = $\underset{x\to {\text{0}}^{\text{+}}}{\text{lim}}\frac{\text{1}}{\text{x}}$ = + ∞ ⇒ Right hand limit of f(x) at 0 does not exist. = $\underset{x\to {\text{0}}^{\text{–}}}{\text{lim}}\frac{\text{1}}{\text{x}}$   x   - 1   - 0.5   - 0.2   -10-1   10-2   …   -10-n   f(x)   - 1   - 2   - 5   -101   -102   …   -10n ⇒ For a negative real number very close to 0, the value of the function will be a very small number. = $\underset{x\to {\text{0}}^{\text{+}}}{\text{lim}}\frac{\text{1}}{\text{x}}$ = – ∞ ⇒ Left hand limit of f(x) at 0 does not exist. The nature of the function f(x) = tan x   xo   tan xo   0°   0   45°   1.0000   60°   1.7320   85°   11.4300   89°   57.2899   89.9°   572.9572   89.99°   5729.5778   89.999°   57295.7795   89.9999°   572957.7951   90°   Infinity ⇒ For an angle very close to 90° from the left side, the value of the function will be a large number. This number is represented by + ∞. = = + ∞   xo   tan xo   180°       0   150°   - 0.5773   120°   - 1.7320   100°   - 5.6712   91°   - 57.2899   90.1°   - 572.9572   90.01°   - 5729.5778   90.001°   - 57295.7795   90.0001°   - 572957.7951   90°   Infinity ⇒ For an angle very close to 90° from the right side, the value of the function will be a small number. This number is represented by – ∞. = = – ∞

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