Find the differential, dy, of y = f(x) = tan(3r²). 1. dy 2. dy 3. dy 4. dy = = = 3 sec²(3x²) tan(3x²) + dx = 6x sec²(3x²) dx 5. dy= 6x sec² (3x) + dx 3 sec²(3x²) tan (3x²) 3 sec²(3r²) tan(3r²) dr dx

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A: Step 1:Step 2:

Q: :1 S* d(x³). 3

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A: limx→∞0.02x350x2=limx→∞0.02x50=∞    Therefore, 0.02x3, will dominates over 50x2

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Q: If E[X] = −3 and Var(X) = 5, then E[(5 + 6X)²] = and Var(3 + 5X) =

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Q: Let X1, X2, X3 and X4 be a random sample from population with pdf X, 0 < x < 1 fx(x) = |0,…

A: Given information: The probability distribution function is fXx=x,    0&lt;x&lt;10,    otherwise.

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Q: Suppose that an = 4" a₁x² + 2a₂x³ + 3a3x4 + 4a4x³. as 00 (i) f(n)x+2 n=0 00 (ii) Σ g(n)x¹+1 n=1 00…

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A: Solution

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A: GivenE(X)=4Var(X)=1

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A: x-2-1012f(x)-10-21-1g(x)210-10The values of different functions at different inputs are given

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A: Γ(x)=∫0∞tx-1e-tdt  for x&gt;0Γ(x+1)=∫0∞txe-tdt =-txe-t0∞+x∫0∞tx-1e-tdt=xΓ(x)⇒Γ(x)=Γ(x+1)x Now,…

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Q: Given g(x) = ex, evaluate each of the following. (a) g(In 3) (b) g[In (62)] (c) g In

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A: Given information: Let X be any continuous random variable. The probability density function of X is…