Use Simpson's 1/3 rule with (n₁ = 2), and Simpson -2 1 estimate tan-¹(2). [Hint: tan-¹ (2) = ₁²; dxl

Q: Let y = 2 ln x - 1/2x then the first derivative is....., the first order condition is..... and the…

A: Given: y=2 ln x-12x To Find:  To determine the first order derivative.To determine the first order…

Q: n(3x)+sin(5x - 4) - 3 Using Centered Differencing. h = 0.002 O 4.86693212 O 4.876145534 D…

A: Equation is f(x) = ln(3x) + sin(5x - 4) - 3

Q: given: y= ln(secx+tanx) find y’’’

A: The given function is y=ln (secx+tanx). Evaluate the derivative of the given function as follows.…

Q: Let f(x) = | 1°dt. Evaluate the following. f'(x) = f'(-6) =

A: ∫xn dx   xn+1 /n+1 + C f(x) = ∫x0 t6 dt       = [t7/7]x0   f(x) = x7/7

Q: use the table to estimate the 10.2 10.3 5.6 4.3 4.7 4.2 10 10.1 (x) 4.5 3.4 g'(x) 6.5 5.9 9 Sunday

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Q: The central difference approximation to the derivative ƒ(x) = x² sin(2x) at x = π/3 is: (use step…

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Q: The backward difference approximation to the derivative f(x) = x² sin(2x) at x = π/3 is: (use step…

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Q: Use three-point midpoint formula to evaluate the first derivative of y=tan(x) at x = O-2√/2 00…

A: Given function is y=tanx. We have to evaluate the first derivative of y=tanx at x=π4 using a value…

Q: P(t)is the population of Mexico (in millions), where t represents the number of years since 2000.…

A: To explain: The meaning of P'(5)=1.5.  Given information: The expression P(t) represents the…

Q: For the function f(x) = 2* we use the two-point formula to approximate the first derivative of f at…

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Q: d -(tan²(x) - dx 1 Prove that : 1+x*

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Q: Given that f(x) = x²h(x) h( – 1) = 4 h'( – 1) = 7 Calculate f'( – 1). Hint: Use the product rule and…

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Q: Find the theoretical error bound in approximating SN" sin(x?) dx using Boole's Rule.

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Q: Let f(x) = 3x ex − cos x. Use the data in the following table and the formula for the second…

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Q: Let f(x) = t° dt. Evaluate the following. f'(x) = f'(5)

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Q: The forward difference approximation to the derivative f(x) = x² sin(2x) at x = π/3 is: (use step…

A: The forward difference approximation to the derivative f(x) = x2 * sin(2x) at x= π/3 (use step size…

Q: Find the equation of the tangent line of f (x)= x² In x at x=1.

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Q: Find the derivative of f(x)= (Inx Oa 6x(Inx Ob. 4 inx Oc 12(in a Od 24(inx

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Q: aluate the second derivative of fix) = =-5 for x= lect the correct choice below and filin any answer…

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Q: Evaluate the implicit function by finding dy/dx of x³+3y=3xy

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Q: Given the fcn y=t^7(t^3+8)^5. Find dy/dx.

A: Given,           y=t7t3+85

Q: If In = f(In x)" dx, show that In = x(lnx)" - nln-1. Hence find f(In x)³ dx.

A: Given that In=∫ln xndx, we have to show that In=xln xn-nIn-1 and also find the value of ∫ln x3dx.

Q: Find d/dx (x9/10). d/dx (x9/10)= ​(Type an exact​ answer

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Q: Use Dnf (x) to approximate the derivative of f(x) = sin(x) at ;h = (0.01,0.2) 4

A: Given fx=sinx at π4, h=0.01,0.2