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Home Question Bank Math Pre Calculus Archive 2025 January 14

Pre-calculus Questions from Jan 14,2025

Browse the Pre-calculus Q&A Archive for Jan 14,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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3.1 Given the geometric sequence: \( 8(x-2)^{2} ; 4(x-2)^{1} ; 2(x-2)^{4} ; \ldots x=2 \) 3.1.1 Delermine the value( s ) of \( x \) where the sequence converges. 3.1.2 Determine the sum to infinity of the series if \( x=2.5 \). 3.2 Given: \( \sum_{i=1}^{n} 3(-2)^{1-2} \) 3.2.1 How many terms are there in this series? 322 Calevlate the sum of the series. Find the domain of the function \( f(x)=\ln (7-3 x) \). Write your answer using interval notation, The domain of \( f(x) \) is If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \) for which of \( x \) is f \( (x) \) non real \( f(x) \) underfined \( f(x)>0 \) Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \) Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s). EXERCISE 2. Study the monotony of the following sequences: \( U_{n}=\frac{1}{3+n}+\frac{1}{n+4}, U_{n}=-n^{2}\left(1-\frac{1}{n}\right)( \) ex \( ), U_{n}=\frac{\sqrt{2+2(-1)^{n}}}{n+1} \), \( U_{n}=n\left(n+(-1)^{n}\right)(e x), U_{n}=\sqrt[n]{2}, U_{n}=-n+n^{2}( \) ex \( ) \). The accompanying bar graph shows the net earnings (in millions of dollars) for a certain company. The polynomial \( 6.30 x^{3}-178.9 x^{2}+1785 x-5532 \) gives a good approximation of the company's net earnings in year \( x \), where \( x=7 \) corresponds to 2007 , and so on \( (7 \leq x \leq 16 \) ). (a) Use the bar graph to determine the net earnings in 2010 . (b) Use the polynomial to determine the net earnings in 2010 . 9. مساله مقدار اوليه را در بازء داده شده حل كنيد. (ץ نمره) الف. ب. \( x y^{\prime}+y=y^{2} x^{2} \ln x \) در بازء ( \( \mathrm{y}=0.5 \) كه به ازاى x=1 داريم QUESTION 3 The equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \). Write down the equation of the new function that is formed when \( f \) is transformed as follows: \( 3.1 \quad \) Shift two units to the left \( 3.2 \quad \) Shift 3 units up \( 3.3 \quad \) Shift 1 unit right and 2 units down \( 3.4 \quad \) The equation of the new hyperbola has new asymptotes at \( x=-4 \) and \( y=-1 \) QUESTION 4 Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \) Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s). QUESTION 3 The equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \). Write down the equation of the new function that is formed when \( f \) is transformed as follows: \( 3.1 \quad \) Shift two units to the left \( 3.2 \quad \) Shift 3 units up \( 3.3 \quad \) Shift 1 unit right and 2 units down QUESTION 4 The equation of the new hyperbola has new asymptotes at \( x=-4 \) and \( y=-1 \) Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \). Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s). Coalcula por triangularizacão a) \( \left|\begin{array}{cccc}2 & -3 & 1 & 7 \\ -2 & 3 & 0 & 4 \\ -1 & 5 & 4 & -3 \\ 2 & 4 & -5 & 0\end{array}\right| \)
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