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Home Question Bank Math Calculus Archive 2025 January 01

Calculus Questions from Jan 01,2025

Browse the Calculus Q&A Archive for Jan 01,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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11) \( f(x)=\left(x^{2}-4\right)^{2} \) fonksiyonunun artan olduğu aralıklar hangisidir? A) \( (-2,0) \) ve \( (2, \infty) \) B) \( (-2,0) \) ve \( (-\infty,-2) \) C) \( (-2,0) \) ve \( (0,2) \) D) \( (2, \infty) \) ve \( (-\infty,-2) \) E) \( (2, \infty) \) ve \( (0,2) \) 24) \( \lim _{x \rightarrow 4} \frac{2-\sqrt{x}}{x^{2}-16}= \) ? \( \begin{array}{lllll}\text { A) }-\infty & \text { B) } \frac{1}{32} & \text { C) } 0 & \text { D) }-\frac{1}{32} & \text { E) Limit yoktur }\end{array} \) 25) \( \lim _{x \rightarrow 0} \frac{|x-2|}{x-2}= \) ? \( \begin{array}{lllll}\text { A) }-\infty & \text { B) Limit yoktur } & \text { C) } 1 & \text { D) } \infty & \text { E) }-1\end{array} \) 1) \( y=\cos ^{-1}(\sin x) \Rightarrow y^{\prime}=? \) A) \( -\frac{\cos x}{|\cos x|} \) B) \( \frac{\cos x}{|\cos x|} \) C) \( -\frac{\cos x}{\sqrt{1-x^{2}}} \) D) \( \frac{\cos x}{\sqrt{1-x^{2}}} \) E) \( -\frac{\sin x}{\sqrt{1-x^{2}}} \) 2) \( \left.\frac{d}{d x} \cot ^{-1}(a x+b)\right|_{x=-b / a}=? \) A) \( a \) B) \( b \) C) \( -a \) D) \( -b \) E) \( a / b \) b) (i) Consider the infinite geometric series \( \sum_{n=1}^{\infty} 10\left(1-\frac{3 x}{2}\right)^{n} \) for what does a sum to infinity exist? (ii) Find the sum of the seriec if. \( F(x)=\int_{1}^{\pi} \frac{\cos t}{t} d t \) siendo \( x \geq 1 \) \( F(x)=\int_{1}^{\pi} \frac{\cos t}{t} d t \) siendo \( x \geq 1 \) 14) If \( y=\sin x+\sec x, x=3 \pi z \), then \( \frac{d y}{d z}=\ldots \ldots \ldots \). At \( z=1 \) \( \begin{array}{llll}\text { a) } 3 \pi & \text { b) }-3 \pi & \text { c) }-6 \pi & \text { d) }-1\end{array} \) b Determine the critical points of the function \[ f(x)=\left\{\begin{array}{ll}x^{3}+6 x^{2} & \text { if } x \leq 0 \\ x^{2}-4 x & \text { if } x>0\end{array}\right. \] in the interval \( [-7,7] \). A \( (-4,32),(0,0),(2,-4) \) B \( (-7,63),(-4,0),(0,0),(2,0),(7,10) \) C \( (-4,0),(0,0),(2,0) \) D \( (-7,63),(0,0),(7,21) \)
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