Post mathematic related questions here

[ACidBaseD]

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NEW OBJECTIVE QUESTION

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Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
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you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋

I am getting ans = -2
By using L'Hospital Rule then opening the Determinant and using limits respectively on each summation term

 

[rst]

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NEW OBJECTIVE QUESTION

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Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋

 

[rst]

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NEW OBJECTIVE QUESTION

*img818.imageshack.us/img818/1681/f3ry.png

Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋

 

[rst]

if f(x)=|x-2| + |x+1|-x then find value of f ' (-10)

 

[Superayush]

Is it given x belong to which domain?

 

[rst]

Is it given x belong to which domain?

domain is not given

options are
(a) -3 (b) -2 (c) -1 (d) 0

 

[avj]

(a) -3
d/dx of |x| is |x|/x and obviously x != 0

- - - Updated - - -

Is it given x belong to which domain?

x=-10 so in the domain (-inf,-1)

- - - Updated - - -

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NEW OBJECTIVE QUESTION

*img818.imageshack.us/img818/1681/f3ry.png

Plz explain your answer

(Also you can ask your mathematics related questions or queries
we will try to solve them)
----------------------------------------------------------------------------------------------------------------------
you can use following mathematic symbols(just do copy and paste)
£ ω ∴ ∂ Φ γ δ μ σ Є Ø Ω ∩ ≈ ≡ ≈ ≅ ≠ ≤ ≥ • ~ ± ∓ ∤ ◅∈ ∉ ⊆ ⊂ ∪ ⊥ ô ∫ Σ → ∞ Π Δ Ψ Γ ∮ ∇∂ √ °α β γ δ ε ζ η θ ι κ λ ν ξ ο π ρ σ τ υ φ χ ψ
x⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁿ
x₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋

the function is 1 at x=0 and 2/pi at x=pi/2

and we know that def. integrals is nothing but area under the graph

so consider 2 rectangles with width pi/2 and height 1 and 2/pi.
it is obvious that (sin x)/x integral lies between area of these 2 rectangles since (sin x )/x is monotonically decreasing function in this range(1st derivative test).

so option 1 is right.

 

[rst]

^^ Thanks a lot avg

 

[rst]

What will be remainder if (16 ! +1) is divided by 17 ?

 

[rst]

What will be remainder if (16 ! +1) is divided by 17 ?

We have that 16!≡−1(mod 17) by Wilson's Theorem.

therefore 16! +1 ≡ 0 (mod 17)

So remainder is 0

 

[rst]

what is inverse of y = 5 ^ logx

 

[powerhoney]

what is inverse of y = 5 ^ logx

y=Antilog((log x)/(log 5))???

 

[powerhoney]

Or is it Y=5^x???

 

[seamon]

^^Asking or answering?

 

[powerhoney]

^^Asking or answering?

Answering but sorry, y=5^x is wrong... You could do???

 

[powerhoney]

I could only do till log x Base 10= log y Base 5

 

[powerhoney]

Is the answer y=10^(log x base 5)???

 

[powerhoney]

Answering but sorry, y=5^x is wrong...
Could you solve???

.....

 

[rst]

what is inverse of y = 5 ^ logx

y = 5 ^ log x

log_5 y =log x ,( Here log_5 y is log y Base 5)

e^(log_5 y) = x

e^(log y /log 5) = x

(e^log y ) ^(1/log 5) = x

y ^(1/log 5) = x

 

[powerhoney]

y = 5 ^ log x

log_5 y =log x ,( Here log_5 y is log y Base 5)

e^(log_5 y) = x

e^(log y /log 5) = x

(e^log y ) ^(1/log 5) = x

y ^(1/log 5) = x

Er, I think I got the same answer... You took base e and I took base 10... Also, I represented inverse as we were taught by switching 'x' and 'y'...