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Home Question Bank Math Calculus Archive 2024 November 02

Calculus Questions from Nov 02,2024

Browse the Calculus Q&A Archive for Nov 02,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Califique con verdadero o falso las siguientes proposiciones. Justifique su respuesta. a) \( q \) : Si el punto \( P(4,5) \) es punto vacio de la gráfica de \( g \) entonces \( \lim _{v \rightarrow 4} g(v)=5 \). b) \( t: k \neq 0 \wedge a<0 \Longrightarrow 4 a k^{2}>5 a k^{2} \) c) i: Si \( G: G(t)=\frac{H(t)}{t+1} \), H es inpar y \( H(3)=11 \) entonces \( \left(-3, \frac{11}{2}\right) \in G \). 1. Given that \( \int \cos x d x=\sin x \) find a. \( \int \cos (2 x+1)= \) 2. Determine se a sequência é monótona e limitada. \( \begin{array}{llll}\text { a) }\left\{\frac{2 n-1}{4 n-1}\right\} & \text { d) }\left\{\frac{n^{3}-1}{n}\right\} & \text { g) }\left\{\frac{n!}{3^{n}}\right\} & \text { j) }\left\{\frac{n!}{1 \cdot 3 \cdot 5 \cdot 7 \ldots(2 n-1)}\right\} \\ \text { b) }\left\{\frac{1-2 n^{2}}{n^{2}}\right\} & \text { e) }\left\{\frac{1}{n+\operatorname{sen} n^{2}}\right\} & \text { h) }\left\{\frac{n^{n}}{n!}\right\} & \text { L) }\left\{\frac{1 \cdot 3 \cdot 5 \cdot 7 \ldots(2 n-1)}{2^{n} \cdot n!}\right\} \\ \text { c) }\{\operatorname{sen} n \pi\} & \text { f) }\left\{\frac{2^{n}}{1+2^{n}}\right\} & \text { i) }\left\{\frac{n}{2^{n}}\right\} & \text { m) }\left\{\frac{1 \cdot 3.5 \ldots . .(2 n-1)}{2 \cdot 4.6 .8 \ldots(2 n)}\right\}\end{array} \) tiven that \( \int \cos x d x=\sin x \) find (a) \( \int \frac{\cos (2 x+1)}{2} d x+c=\cos u \) (Ingreso marginal) si la ecuación de demanda es \( x^{\frac{3}{2}}+5 p=1000 \), Calcule elingreso marginal cuando \( p=16 \) 1). \( \int_{0}^{2} \int_{1}^{3}\left(x^{2} y-3\right) d y d x \) En los siguientes problemas use la inversa del segundo teorema d slación para encontrar la \( \mathcal{L}^{-1}\{F(s)\} \). F. \( F(s)=\frac{s e^{-\frac{n s}{2}}}{s^{2}+4} \) \( 2 y^{\prime \prime}-3 y^{\prime}-2 y=0, y(0)=0, y^{\prime}(0)=\frac{5}{2} \) el valor de \( Y(1) \) es A box with no top is to be made from a square piece of cardboard with side length 10 inches by cutting out squares from each corner and folding up the sides. If the side length of each cut square is x, what value of x maximizes the volume of the box? (Provide critical points for maximization.) Compute each sum below. Give exact values, not decimal approximations. If the sum does not exist, click on "No sum". \[ 4\left(-\frac{1}{4}\right)+4\left(-\frac{1}{4}\right)^{2}+4\left(-\frac{1}{4}\right)^{3}+\ldots=\prod \] \( \sum_{k=1}^{\infty} 2\left(-\frac{3}{5}\right)^{k}=\square \)
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