Limit and trigonometry (2)

Calculus Level 3

R = sec ⁡ x 2016 , M = csc ⁡ x 2016 , T = cot ⁡ x 2016 \large R =\frac{\sec{x}}{2016}, \qquad M =\frac{\csc{x}}{2016}, \qquad T =\frac{\cot{x}}{2016}

lim ⁡ x → 0 + R M T = ? \large \lim_{x\rightarrow0^{+}} RMT = \, ?

1 − ∞ -\infty Undefined 0 ∞ \infty

Tommy Li by Tommy Li , 22, Hong Kong

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1 solution

Tommy Li
Aug 3, 2016

R = sec ⁡ x 2016 , M = csc ⁡ x 2016 , T = cot ⁡ x 2016 \large R =\frac{\sec{x}}{2016}, \qquad M =\frac{\csc{x}}{2016}, \qquad T =\frac{\cot{x}}{2016}

lim ⁡ x → 0 + R M T = lim ⁡ x → 0 + sec ⁡ x csc ⁡ x cot ⁡ x 201 6 3 \large \lim_{x\rightarrow0^{+}} RMT = \lim_{x\rightarrow0^{+}}\frac{\sec{x}\csc{x}\cot{x}}{2016^3}

lim ⁡ x → 0 + R M T = ( 1 ) ( ∞ ) ( ∞ ) 201 6 3 \large \lim_{x\rightarrow0^{+}} RMT = \frac{(1)(\infty)(\infty)}{2016^3}

lim ⁡ x → 0 + R M T = ∞ 201 6 3 \large \lim_{x\rightarrow0^{+}} RMT = \frac{\infty}{2016^3}

lim ⁡ x → 0 + R M T = ∞ \large \lim_{x\rightarrow0^{+}} RMT = \infty

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