limx-π/2 cot x/π/2-x
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limx→π2cot(π2)-cot(x)π2-x
Evaluate the limit of the numerator and the limit of the denominator.
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Take the limit of the numerator and the limit of the denominator.
limx→π2cot(π2)-cot(x)limx→π2π2-x
Evaluate the limit of the numerator.
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0limx→π2π2-x
Evaluate the limit of the denominator.
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00
The expression contains a division by 0. The expression is undefined.
Undefined
Since 00 is of indeterminate form, apply L'Hospital's Rule. L'Hospital's Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.
limx→π2cot(π2)-cot(x)π2-x=limx→π2ddx[cot(π2)-cot(x)]ddx[π2-x]
Evaluate the limit of the numerator and the limit of the denominator.
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Take the limit of the numerator and the limit of the denominator.
limx→π2cot(π2)-cot(x)limx→π2π2-x
Evaluate the limit of the numerator.
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0limx→π2π2-x
Evaluate the limit of the denominator.
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00
The expression contains a division by 0. The expression is undefined.
Undefined
Since 00 is of indeterminate form, apply L'Hospital's Rule. L'Hospital's Rule states that the limit of a quotient of functions is equal to the limit of the quotient of their derivatives.
limx→π2cot(π2)-cot(x)π2-x=limx→π2ddx[cot(π2)-cot(x)]ddx[π2-x]
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