Example :- Find the deflection u (x,t) velocity string length L= n, C²=1, its ends fixed if the initial deflection f(x) and the initial velocity g(x) are:- 1- f(x) = 0 g(x) = 0.1 sin 2x II

Q: The graph of y = f(x) has a y – intercept of 3 and the tangent line at the point (x, y) has an x-…

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Q: 5) Determine the equation of the tangent to the curve y = √3x² - 2x at x=1.

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Q: = f(x) g(x) If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = y 6…

A: The given graph of the functions is shown as,Let,Note:  As mentioned in the instruction, we are…

Q: TLP iadade mnts & smt Findf F'(t) =sec(t) (seclE)+ tan (ED), -st < f- FCt) = -<ts f (--7 2.

A: We simplify f'(t) by expanding  To find f(t) we integrate f'(t) C=integrating constant

Q: (a) Find the equation of the tangent line to the curvey 2 sec x- 4 cos x at the point , 2) %3D

A: Since you have posted a multiple  question according to guildlines I will solve first…

Q: poin If g(u) —D V9u + 3 then g' (u) =

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Q: A partical is moving in a straight line with velocity v(t) = 2 sin 2t (m/sec). Then the total…

A: Calculate the distance travelled by substituting 2t=u: ∫03π/42sin2tdt=∫03π/2sinudu…

Q: p(t) -t^3-6t^2-36t. 1. Find the velocity function at v(t) of the object 2. Find all times for…

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Q: (a) Use f(t) = a cos (b(t- c)) + d to model these conditions. (b) Evaluate f(1) and f(7). (a)…

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Q: Q2// A) Derivative following functions by using chain rule m 1) y = Vu, 2) y = 4u, -Va+1 Vx+1

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Q: Let f(x) = e»in(²)+z² _ i) Find the x-values of the stationary points to the curve y = f(x), where 0…

A: The given function is  fx=esinx2+x2

Q: The acceleration of a particle as it moves along a straight line is given by a-21 -1. Ifs 1 and y- 2…

A: Given the acceleration of a particle as it moves along a straight line is given by a=2t-1 m/s2, If…

Q: A particle is moving with acceleration a(t) = 12t + 12. its position at time t = 0 is s(0) = 13 and…

A: Sol:-

Q: The speed of the flaming ball is the rate of change in distance travelled. Hence the speed of the…

A: Sol

Q: x(t) = Find real-valued closed formulas for the trajectory x(t + 1) = Ax(t), where -4 ^-[33] -4…

A: This is an homogeneous linear differential system. We will solve by this using eigenvalues and…

Q: The graph of y = f(x) has a y – intercept of 3 and the tangent line at the point (x, y) has a x-…

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Q: Find f(X) if F(0)=0 and the tangent line at (x,f(x)) has a slope X(x^2+2)^3

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Q: dy 2²+1 Use the quotient rule to find the derivative of the function y = dx О А. dy 1 = 2x(x+ V) –…

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Q: Find derivatives of: 1.) f(t)= 7t          2.) g(x)= 3x-9      3.) h(v)= v3 4.) m(x)= π2

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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: Q3) for f(t) = sec?(6t – 1) and g(t) = tan?(6t - 1) show that %3D f'(t) = g'(t).

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Q: a)Use the second derivative test to determine whether the function has a local maximum or local…

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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.