2. Show that x' is O(x*) but that x* is not O(x'). 3. Show that x log x is O(x²) but that x² is not O(x log x).

Q: For any real number b > 1, and any real numbers x True False log, (x - y) = > 0 and y> 0, it must be…

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Q: X* Q: Prove that the function y- 2 2 x+1+/log Vx+Jx +1 + log satisfies the relationship 2y=x dx

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Q: Q5. Find z (1) 3 log, 2+log, 25-log, 20 = log (2) logą z + logs (2-3) = log, 10 (3) Inz-10.1285

A: As we know from the logarithmic properties: 1). logbxa=a·logbx  where x,b>0, b≠1 2).…

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Q: Derive the following function h) f(t) = e-2t³ + In (2-4t) -log(+³+5t)

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Q: (b) Show that u(#) = log log (1 + l#|") belongs to W(U) but does not belong to L(U).

A: Given: u(x)= log log(1 + |x|^-1 )

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Q: 周 紀 =xlogæ+O(x).

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Q: Suppose f : R → R and g: R+ → R are defined by f(x) = x2 + 1 and g(x) = log x – x². What is go f? O…

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Q: em 8.5. Let a 2 100. We have (x) > log loga.

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Q: Condense Conden se into a single logarithm. 4) 6log § x – 31og § y 4.

A: Given 6log8x-3log8y

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A: f'(x)=?

Q: 19. If logx y + log, x = 2.9 and xy = 128, find x + y. 24 O 20V2 O 36 O 34V 2 O 66

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Q: 1 20. If f(x)= and g(x) logx = 1 what is the domain of y = f(x)g(x)? 8 + x²

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Q: Let ƒ(x) = log₂(x + 1) and g(x) = log₂ (z − 1). Find h(x) = f(x) + g(x). - O a) h(z) = log₂ (21) Ob)…

A: This question is related to Functions, we will solve it using given information.

Q: Differentiate with respect to x:* y = log, (x) :() 2+ In x - In x Option 2 Option 3 2 - In x 1+ In x…

A: As per guidelines we can answer only one question at a time so if you need more answers kindly…

Q: Let h(x) = -2log(3x - 5). Define two functions f(x) and g(x), where h(x) = g(f(x)).

A: Given that,

Q: Prove that (ij) d dx² (log √√g).

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Q: 8. For each function, determine whether that function is 2(x²) and whether it is (x²). 6.a f(x) = x…

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A: Given equation is log1+x=x-12x2+13x3+.....+-1n+1nxn+Rn+! So, Rn+1=-1n+2n+1xn+1 So, maximum relative…

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Q: Solve for x: log, x Vlog, * [A] –6, 1, 6 [B] 0, V6 [C] 0, 1, 6 [D] 1, 6 ||

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Q: Use composition to verity that f (2) = logi(z-5) and g (z) 3 +5 are inverses of each other. Show all…

A: f(x) and g(x) are inverse of each other if (fog)(x) = xand (gof)(x) = x

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Q: g(x) = 2 (log x)< + 5x< log x+ 8x a. Show that g(x) is not O(x²). b. Show that g(x) is O(x³). c.…

A: we have given g(x)=2(logx)2+5x2logx+8xa. logx grows at lesser rate than x we consider Highest degree…

Q: Given 2 log3(x + y) = 2 + log3x + log3 y, show that x² + y² = 7xy.

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Q: Show that || (A(st) + A(s)A(t)) dsdt = 2.x log x + 0(x) as x → 0o. JU(4)| log°x s 2 // |u() dsdı +…

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Q: Let x = log 3 and y = log 4. Express the following in terms of x and y.     Please provide all…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: