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Home Question Bank Math Pre Calculus Archive 2024 November 21

Pre-calculus Questions from Nov 21,2024

Browse the Pre-calculus Q&A Archive for Nov 21,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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2) \( \left(w_{n}\right) \) a pour terme général : \( w_{n}=4^{n}-5^{n} \) Sxercice 2: (5 points) Soit \( \left(u_{n}\right) \) la suite définie par \( u_{0}=-3 \) et pour tout \( n \in N \) par \( u_{n+1}=\frac{9}{6-u_{n}} \). Soit \( \left(v_{n}\right) \) la suite définie par \( v_{n+1}=\frac{1}{u_{n}-3} \) 1) Démontrer que la suite \( \left(v_{n}\right) \) est arithmétique de raison \( \frac{-1}{3} \) 2) En déduire l'expression de \( v_{n} \) puis de \( u_{n} \) en fonction de \( n \). 3) Déterminer la limite de la suite ( \( u \) ). Let \( f(x)=7\left(\frac{1}{2}\right)^{x} \). Complete parts (a) through (e) below. (e) Is f a one-to-one function? Does fhave an inverse? Let \( f(x)=7\left(\frac{1}{2}\right)^{x} \). Complete parts (a) through (e) below (c) Find any asymptotes of the graph of \( f \). Select the co Let \( f(x)=7\left(\frac{1}{2}\right)^{x} \). Complete parts (a) through (e) below. (a) What are the domain and range of \( f \) ? The domain of \( f \) is \( \square \) and the range of \( f \) is (Type your answers in interval notation.) (b) Is f either increasing or decreasing on its domain? Graph all vertical and horizontal asymptotes of the \[ f(x)=\frac{8 x-7}{-2 x-1} \] Use the theorems proved in class about induction to evaluate the sums below. (Note that you are begin asked to apply the theorems, not formally proving a new theorem.) a. \( 7+14+21+28+\cdots+350^{\circ} \) b. \( 16+17+18+\cdots+411 \) c. \( 1-\frac{1}{10}+\frac{1}{100}-\frac{1}{1000} \cdots+\frac{1}{10^{18}} \) When the function \( f(x)=\cos x \) is reflected across the \( x \)-axis, the resulting function is \( g(x)=-\cos x \). If the coordinates of the \( y \)-intercept of \( f(x)=\cos x \) are \( (0,1) \), what are the coordinates of the \( y \)-intercept of the reflected function \( g(x) \) ? (1 point) \( (1,0) \) \( (-1,0) \) \( (0,-1) \) \( (-1,1) \) The table contains values for \( f(x) \). If \( h(x) \) is the reflection of \( f(x) \) across the \( x \)-axis, find the missing value in the ordered pair below, for \( h(x) \). \( x \quad-\frac{\pi}{2}-\frac{\pi}{4} \) \( f(x) \) 0 1. Write the following sets as an interval or union of interval. In each case \( x \in \Re \). a) \( A=\{x: x \neq 0 \wedge x \neq 8\} \) b) \( B=\left\{x: x^{2}\left(x^{2}-1\right) \neq 0\right\} \) c) \( B=\left\{x: x^{2}=2 \Leftrightarrow x \geq-1\right\} \) d) \( C=\left\{x:\left(x^{3}-2 x\right) \neq 0\right\} \) e) \( C=\{x:(x-2)(x+3)=0 \Rightarrow x \geq 0\} \) Part 2 of 5 A campground owner has 2500 m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing along the river. (See the s 0.71 of 1 (a) Write an expression for the length of the field as a function of \( x \). (b) Find the area of the field (area \( = \) length \( \times \) width) as a function of \( x \). (c) Find the value of \( x \) leading to the maximum area. (d) Find the maximum area. (a) \( \ell(x)=2500-2 x \) (b) \( A(x)= \)
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