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- how to find the bounds of y=sin(x) y=cos(x) x=0Explain the following questions in detail how to solve with detailed Explanation. 1. Evaluate integral(upper limit=1/2 , lower limit=0) x4(1-2x)3dx using beta or gamma function.1. Evaluate: lim x→2 (x^2 − 4x + 4)/(tan^2(x2 − 4)) 2. Use the Intermediate Value Theorem to show that f(x) = cos^−1 (x) − e^x has a zero in the interval [0, 1]. 3. Use the Squeeze Theorem to evaluate: lim x→0+ sin(ln x) csch(cot x).
- Evaluate Z 3π2πe1x sin x cos x dxusing Simpson rule with h =π20.Use the closed interval method to find the absolute maximum and absolute minimum of f(x)= 2 cos x+ sin 2x of the interval [0,π/2]Why does the limit as x goes to 0 of cos(1/x) not exist? Can use two different sequences: xn=1/(n*pi), and yn=2/((2n+1)pi) and show that lim cos(1/xn) ≠ lim cos(1/yn).