Verify the initial value theorem of f(t) = 1 +e¯t[sint + cos os t]. 3 1 0 2
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![Verify the initial value theorem of f(t) = 1 + e¯t[sint + cost].
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Verify the initial value theorem of f(t) = e(t + 2)².
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- A particle moving along a line has position s(t) = t4 − 18t2 m at time t seconds. At which times doesthe particle pass through the origin? At which times is the particle instantaneously motionless (i.e., it has zerovelocity)?Use a linear approximation function L(x) to estimate f(4.1) given that f(4) = 6 and f′(4) = −2. Check your solution using the differential dy = f′(x)dx.A stone, projected vertically upward with initial velocity 112ft/sec, moves according to s = 112t − 16t2, where s is the distance from the ground. When will it reach the maximum height?
- Find dy/dx for e 2x + y 2 = sec(2x) in terms of x and y using implicitdifferentiationA particle moving along a line has position s(t) = t 4 - 18t2 m at time t seconds. At which times does the particle pass through the origin? At which times is the particle instantaneously motionless (i.e., it has zero velocity)?Find the differential dy of the given function. Y= square root 7- x^2 Dy=?
- Find the particular antiderivative of the following derivative that satisfies the given condition. dx/dt= 5e^t -3 ; x(0)=4Find the DE by eliminating the arbitrary constant y = A+ bexA particle initially situated at the origin moves along the x-axis so that its acceleration at any time t is given by a(t) = 2t - 7. If the initial velocity of the particle is 6, at what time t during the interval is the particle farthest to the right?
