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Home Question Bank Math Pre Calculus Archive 2025 January 21

Pre-calculus Questions from Jan 21,2025

Browse the Pre-calculus Q&A Archive for Jan 21,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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7 Determine the number of terms: a \( \quad x(1+i) ; x(1+i)^{2} ; x(1+i)^{3} ; \ldots ; x(1+i)^{40} \) b \( \quad x(1+i)^{-1} ; x(1+i)^{-2} ; x(1+i)^{-3} ; \ldots ; x(1+i)^{-160} \) c \( \tan x ; \sin x ; \sin x \cos x ; \ldots ; \tan x(\cos x)^{9} \) d \( 1 ; \sin x ; 1-\cos ^{2} x ; \ldots ;(\sin x)^{11} \) 8 Given \( \mathrm{T}_{n}=\frac{3}{8}(r)^{n-1} \) for a geometric sequence. a If the 4th term is \( \frac{81}{8} \), calculate the value of \( r \). b Which term is equal to \( \frac{59049}{8} \) ? 7 Determine the number of terms: a \( x(1+i) ; x(1+i)^{2} ; x(1+i)^{3} ; \ldots ; x(1+i)^{40} \) b \( x(1+i)^{-1} ; x(1+i)^{-2} ; x(1+i)^{-3} ; \ldots ; x(1+i)^{-160} \) c \( \tan x ; \sin x ; \sin x \cos x ; \ldots ; \tan x(\cos x)^{9} \) d \( 1 ; \sin x ; 1-\cos ^{2} x ; \ldots ;(\sin x)^{11} \) 6 Calculate the value of the \( n \)th term. a \( \quad x(1+i) ; x(1+i)^{2} ; x(1+i)^{3} ; \ldots \) b \( x(1+i)^{-1} ; x(1+i)^{-2} ; x(1+i)^{-3} ; \ldots \) c \( \tan x ; \sin x ; \sin x \cos x ; \ldots \) d \( 1 ; \sin x ; 1-\cos ^{2} x ; \ldots \) domain and range \( h(x)=\left\{\begin{array}{ll}x^{2}, & -3 \leq x<3 \\ 2-x, & 3 \leq x<7\end{array}\right. \) Describe the end behavior of the function. \( f(x)=11-18 x^{2}-5 x^{3}-12 x^{4}-2 x \) 3 Consider the geometric series: \( 45+15+5+\ldots \) 3.1 Does the sequence converge or diverge? Justify your answer. 3.2 Determine the sum to infinity of the series, if it exists. 1 Determine the sum to infinity for each of these geometric series: \( 1.136+12+4+\ldots \) \( 1.2-20-5-1,25-\ldots \) \( 1.3 \quad 40-20+10-5+\ldots \) \( 1.4 \quad-27+18-12+8-\ldots \) 3 Consider the geometric series: \( 45+15+5+\ldots \) 3.1 Does the sequence converge or diverge? Justify your answer. 3.2 Determine the sum to infinity of the series, if it exists. Describe the general shape of the graph for the inverse sine function, \( y = \sin^{-1}(x) \), including its domain and range. For each equation below, determine if the function is Odd, Even, or Neither \( f(x)=\sqrt{x} \) Select an answer \( \checkmark \) \( g(x)=\frac{2}{x} \) Select an answer \( \checkmark \) \( h(x)=x^{2}+2 \) Select an answer \( \checkmark \) Question Help: Video Submit Question
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