4. A 10-kg mass is attached to a spring having a spring constant of 140 N/m. The mass is started in motion from the equilibrium position with an initial velocity of 1 m/sec in the upward direction and with an applied external force F(t) = 5 sin t. Find the subsequent motion of the mass if the force due to air resistance is -90ù N.

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A: Inverse of function y= f(X) is defined as the  X = f-1 (y)

Q: 1 If y = V1-x then y' = 2/1-x

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Q: What are application of 1st principle method of derivative?

A: First principle method: Differentiation from first principles: Given a function y=f(x) its first…

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A:

Q: хах Vx2-6х +13

A: Let I is the value of given Integral.

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A:

Q: What’s the difference between differential and inferential Calculus? And How do they apply to…

A: DIFFERENCE BETWEEN INFERENTIAL AND DIFFERENTIAL CALCULUS:…

Q: Solve each of the following differential equations: (a) f'(t)-f(t) = 2 where f(0) = 0 (b) f'(t) +…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Optimize the function f(x,y) = x^2+y^2 given the condition of x=y^2-5.

A: Answers are following in explanation step.Explanation:

Q: * 31² +t+4 dt t' +t

A:

Q: du _ dv dy dx If f(z) =z²+z - ,2

A: Take z= X+iY and proceed

Q: compute the derivate

A:

Q: Now, differentiate the function y' = 4x(1 + 2 In). y" = 4 + 8 + In + 8 In

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Q: j(1+j3/1-j3)^2

A:

Q: What is the derivatives of f(x)=(x^3)/(9-X^2) and its x and y intersect?

A: a) From the given problem: fx=x39-x2Ory=x39-x2   So,   dydx=ddxx39-x2=ddxx39-x2-ddx9-x2x39-x22…

Q: what is the gradient of f(x)=3x2-2x at x=-2?

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Q: 23 dt de L²₁ (326 -t) dr

A:

Q: find d/dx 2x^2 -x using derication from first principle through the use of (f(x+h)-f(x))/h

A: Topic = Derivative

Q: Explain the benefit of L’Hôpital’s Rule.

A: L'Hopital's rule is the rule to determine  the limit of any given function, which is almost…

Q: (ii) Show that {Xt} is stationary.

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Q: As an application of partial derivative of multi-variable functions, provide one page about Lagrange…

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Q: Evaluate y' if y = vtan x

A: We solve the problem by doing the derivative using the formula.