what is the ratio between b (n) and a (n):

Q: What is the derivative of y= 3Arcsin xº, 3 Arcsin x In 3 A y' = 1 - xa 3 Arcsin x* In 3 3 B y' : (а…

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Q: Jo 8-7. Find the derivative of the functions: (a) h(x) = | In(t) dt g(x) = [" (c) dz 24 +1 3r (b)…

A: Solution: The objective is to find the derivative of the given function

Q: A table of values for an invertible function f, and its derivative f' is given: x f(x) f'(x) | 2 2…

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Q: Use linear approximation, i.e. the tangent line, to approximate 1001 as follows: Let f(x)=³. The…

A: Using the given formula

Q: A) find the derivatives for the following: 1) y = In(In(sin¯'(e?r))) – 5-Inx 2) Y=sech-1(log, 93*) +…

A: Chain rule for differentiation: Let y=fghx then dydx=ddxfghx=dfghxdghx×dghxdhx×dhxdx Equation of…

Q: For 0 ≤ t ≤ 3, the velocity of an object is given by v (t) = 4 — et centimeters per second. The…

A: Since we have s(t) =4t-e^(t) +CAlso we have s(0) =5

Q: Find the first and second derivative of the function. G(r) = Vr + Vr 1 + 1 G'(r) = 3x G"(r) =

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Q: 11. 7(t) = (cost, e¹, Int)

A: Given rt=cost,et,lnt We know that dcostdt=-sintdetdt=etdlntdt=1t

Q: 2) Students often make these simple derivatives harder than necessary. How would you differentiate…

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Q: Find any relative maxima and relative minima. relative maximum (x, y) = relative minimum (x, y): %3D…

A: The given function is - y = x(x-5)2y' = -x+5(x-5)3y'' = 2x+20(x-5)4

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 16) y = (x2 - 2x + 1) eX B) (x2…

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Q: Q3) Find the derivative of y for all functions the following (1) y = 0 (sin (In 0) + cos (In 0)),…

A: Since you have posted multiple questions, we have solved the first question for you, if any specific…

Q: 26 Functions f(a) and g(x) and their first and second derivatives evaluated at z = 1 are listed as…

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Q: 1) Circle the two equations for which the use of logarithmic differentiation would be most…

A: We can differentiate the functions in options (a) and (b) directly by using standard formulas. So no…

Q: For the function f(x) = 5x° - 3x + 2x + 7x + 3, find f"(x), the third derivative of f, and f4) (x),…

A: Third and Fourth derivative of f(x): f3x=300x2-74x+12f4x=600x-74

Q: x f(x) f'(x) g(x) g'(x) 1 1 1 3 3 4 3 65 1 3 -2 3 4 4-2 -6 51 6 The functions f and g have…

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Q: Q2] Solve only Two a) Use the Chain rule to find the derivative of z= e*y with respect to t if x=t…

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Q: Consider the function f(x) = 3x4 -83+6x2 – 1. Use calculus to determine (a) the intervals where the…

A: Given query is to find critical points, maximum, minimum, inflection points for the function.

Q: 3 Ay The graph of y = x²(x + 3) and y= (x > 0) intersect at one point, x = r, as shown to the right.…

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Q: Find the equation of the tangent line to the graph of the given function at the given value of x. 2…

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Q: 4) Knowing that f = f(t), using the expressions of L[f'] and L[f"], derive an expression for d'f…

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Q: 3, Let f (x) = Vx – 7. Find f 1 Of ' (z) = - Of'(z) = -V – 7 %3D 1 Of (x) = a° + 7 Of (x) = (x + 7)³…

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Q: -3 A curve has for its third derivative equals to x If (1, -1) is a point of inflection of " the…

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Q: Halley's method is an improved Newton's method where the second derivative of a function f (x) is…

A: Halley's Method: The formula to find the root of f(x) is given as…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.