WebApr 11, 2024 · If f(x) + f(π – x) = π 2 then \(\int\limits_0^\pi\) f(x) sin x dx (1) ... Let f(x) = (k cos x)/(π - 2x) when x ≠ π/2 and if lim(x→π/2) f(x) = f(π/2), find the value of k. asked Sep 12, 2024 in Limits by Shyam01 (50.9k points) limits; derivatives; class-11; 0 votes. 1 answer. WebIf \\( f(x)=\\left\\{\\begin{array}{cl}\\frac{\\cos ^{2} x-\\sin ^{2} x-1}{\\sqrt{x^{2}+1}-1}, & x \\neq 0 \\\\ k, & x=0\\end{array}\\right. \\) is continuous ...
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WebUsing this formula, subtract sin^2x from both sides of the equation, we have sin^2x + cos^2x -sin^2x = 1 -sin^2x which implies cos^2x = 1 - sin^2x. Two trigonometric formulas that includes cos^2x are cos2x formulas given by cos2x = cos^2x - … WebThe derivative of sin 2 x is sin 2x. Let us see how. Let f(x) = sin 2 x. This can be written as f(x) = (sin x) 2. To find its derivative, we can use a combination of the power rule and the chain rule. Then we get, f'(x) = 2(sin x) d/dx(sin x) = 2 sin x cos x = sin 2x (by using the double angle formula of sin) Therefore, the derivative of sin 2 ... WebThe integral of sin 2x is denoted by ∫ sin 2x dx and its value is - (cos 2x) / 2 + C, where 'C' is the integration constant. For proving this, we use the integration by substitution method. … extracting dna from kiwi method