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OthersQuestion and Answers: Page 11
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Question and Answers Forum |
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OthersQuestion and Answers: Page 11 |
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| Solve the inequalities: ∣x−(1/2)∣>1 Thank you |
| Show that for all a,b∈R i) ab≤(1/2)(a^2 +b^2 ) ii) (((a+b)/2))^2 ≤(a^2 +b^2 ) iii) (√(ab))≤(1/2)(a+b), for a,b≥0 such that a and b have square roots. Help |
| 1) Prove that: ∣a+b+c∣≥∣a∣−∣b∣−∣c∣ 2) Find all x∈R that satify the follow− ing inequalities i) ∣x^2 −4∣<5 ii) ∣x∣+∣x+2∣<5 Help! |
| Show that for all a,b,c,d ∈ R with a,b,c,d ≥ 0 1) (√(ab))(√(cd)) ≤ (1/4)(a^2 +b^2 +c^2 +d^2 ) 2) (abcd)^(1/4) ≤ (1/4)(a+b+c+d) Help! |
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| Show that for a,b∈R, ∣a−b∣≥∣a∣−∣b∣ (Hint: write a=(a−b)+b |
| Find all x∈R that satisfy the following inequalities: a) ∣4x−3∣≤11 b) ∣x−2∣>∣x+1∣ c) ∣x∣ + ∣x+2∣ + ∣2−x∣≤8 |
| 1) Prove that if ε>0 and a,x∈R, then ∣a−x∣<ε iff x−ε<a<x+ε help |
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| Show that the following functions are continous on a close interval [0, 1]. f(x)={_(3 x=1) ^(((x^2 +x−2)/(x−1)) x≠1) Help! |
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| If n is a positive integer, prove that 2^n Γ(n+(1/2)) = 1.3.5...(2n−1)(√π). Help! |
| Let G be the group ({1, ı, −1, −ı}, ∙) and let H ≤ (+_− 1, ∙), show that θ:G→H is an Isomorphism. Hello! |
| Find the supremum and infimum of each of the following sequence a) {((n−1)/(2n))} b) {(((−)^n n)/(2n+1))} c){((1+(−)^n )/3)} d) {sin((nπ)/2)} e) {(1/n) − sin((nπ)/2)} f) {(1+(1/(2n)))cos((nπ)/3)} Help! |
| Prove that the sequence {a_n } is null when {a_n } is given by ((n^3 +2n^2 −1)/(n^4 −n^2 +2)) Help! |
| (1/π)∫_0 ^(2π) xcos(nx)dx Help! |
| find g(f(x)) f(x)=x^3 −x^2 +3x g(x)=x^2 −2x+1 |
| lim_(x→1 ) (3x^2 −7x+3)^(10) find the limit |
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| If f(t) = 2(e^t − 1) a) Does f(t) exists for all n ? b) If it exist, does it converge ? c) If the sequence converge, does the limit converge ? d) Is the solution uniques ? |
| A heat transfer of 9.0×10^5 J is required to convert a block of ice at 20°C to water at 15°C, what was the mass of the block of ice ? |
| The first term of an arithmetic series is 7 and the last is 70. and the sum is 385. find the number of terms in the series and its common difference. |
| The sum of three numbers in arith- metic progression is 18 and sum of square is 206. find the numbers |
| Find the sum of the first 16th term of the series 3(1/2) + 4(3/4) + 6 + 7(1/4) ... |
| Let f:R^3 →R be define by f(x, y, z) = 2x^2 −y+6xy−z^3 +3z. calculate the directional deriva− tive of the vector u=(2, 1, −3) help! |