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Home Question Bank Math Pre Calculus Archive 2025 January 09

Pre-calculus Questions from Jan 09,2025

Browse the Pre-calculus Q&A Archive for Jan 09,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Montrer que pour tout réel \( x \) on a \( \left|\frac{5 x^{2}}{x^{2}+1}-4\right| \leq\left|x^{2}-4\right| \) On suppose que \( |x-2|<\frac{1}{2} \) A- Vérifier que \( |x+2|<\frac{9}{2} \) B- Montrer que \( \left|\frac{5 x^{3}}{x^{3}+1}-4\right| \leq \frac{9}{2}|x-2|<\frac{9}{2} \), que peut-on dé Déterminer le signe de \( |x|+|y|-\sqrt{x^{2}+y^{2}} \) sachant que Compute the following function values for \( f(x)=\left\{\begin{array}{lll}x-9 & \text { if } & x \leq-3 \\ \sqrt{25-x^{2}} & \text { if } & -3<x \leq 3 \\ -x-9 & \text { if } & x>3\end{array}\right. \) Enter exact answers. If the answer is irrational, use the square root symbol from the math tools or type sqrt(\#). \( f(-4)= \) \( f(-3)= \) \( f(3)= \) \( f(3.001)= \) \( f(-3.001)= \) Exercice 2 ।- 3) Montrer que pour tout réel \( x \) on a \( \left|\frac{2 x^{2}}{x^{2}+1}-1\right| \leq\left|x^{2}-1\right| \) 1-2 Plot the point whose two other pairs of polar and one with \( r<0 \). 1. (a) \( (2, \pi / 3) \) 2. (a) \( (1,7 \pi / 4) \) Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{\kappa-1}+1 \) Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s). 1.2 If \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is 1.2.2 \( \quad f(x) \) non real. 1.2.3 \( f(x) \) undefined 1.2.4 \( f(x)>0 \) (2) \( 8+\frac{8}{3}+\frac{8}{9}+\ldots=\frac{8744}{729} \) (4) \( \frac{3}{4}-\frac{3}{8}+\frac{3}{16}-\ldots=\frac{513}{1024} \) 6.1 The first two terms of an infinite geometric sequence are 8 and \( \frac{8}{\sqrt{2}} \). Prove, without the use of a calculator, that the sum of the series to infinity is \( 16+8 \sqrt{2} \) 6.2 The following geometric series is given: \( x=5+15+45+\cdots \) to 20 terms. 6.2 .1 Write the series in sigma notation. Calculate the value of \( x \). he equation of a hyperbola is given by \( f(x)=\frac{5}{x-7}-4 \) rite down the equation of the new function that is formed when \( f \) is transformed as follows: \( 2 \quad \) Shift two units to the left 3 Shift 3 units up Shift 1 unit right and 2 units down \( f(x)=\frac{\sqrt{x+2}}{3-3 x^{2}} \), for which values of \( x \) is 22 \( f(x) \) non real. \( 23 \quad f(x) \) undefined
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