What is \lim_{x\rightarrow\frac{\pi}{2}}(\sec x-\tan x) equal to?
- A. -1
- B. 0 ✓
- C. 1/2
- D. 1
Correct Answer: B. 0
Explanation
Convert the expression to sines and cosines: \lim_{x \to \pi/2} \left(\frac{1}{\cos x} - \frac{\sin x}{\cos x}\right) = \lim_{x \to \pi/2} \frac{1-\sin x}{\cos x}. Using L'Hopital's rule, differentiate the numerator and denominator to get \lim_{x \to \pi/2} \frac{-\cos x}{-\sin x} = \frac{0}{-1} = 0.
Related questions on Calculus
- Let z=[y] and y=[x]-x, where [.] is the greatest integer function. If x is <strong>NOT</strong> an integer but positive, then what i...
- If f(x)=4x+1 and g(x)=kx+2 such that fog(x)=gof(x), then what is the value of k?
- What is the <strong>MINIMUM</strong> value of the function f(x)=\log_{10}(x^{2}+2x+11)?
- What is \int(x^{x})^{2}(1+\ln x)\,dx equal to ?
- What is \int e^{x}\{1+\ln x+x\ln x\}\,dx equal to?