Read and analyze each word problem and give what is/are required. Write the detailed solution If possible, express your final anşwer in the form u(t)= Rcos(@,t – 8). 3. A spring is stretched 1.5" by a 2-lb weight. Let the weight be pushed up 3" above equilibrium and the released. Describe the motion.

Q: そっ tax)= x-3x- Finel (t-'j'(-1)

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

Q: Which expression to (3 + i)(1 - i)? Note i √-1. O4+i O 4 O2 - 2i O4 - 2i is equivalent

A:

Q: хах Vx2-6х +13

A: Let I is the value of given Integral.

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

A: DIFFERENCE BETWEEN INFERENTIAL AND DIFFERENTIAL CALCULUS:…

Q: dve the equa tion Sustainably with Laplace trans forms

A:

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

A:

Q: Integrate (2x - 5) with respect to x from x = 2 to x = 5.

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: Explain what it means if a' . b = 0

A:

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

A:

Q: Differentiate f (x)  = eex

A: f(x)=eex

Q: 3-2 7) 6 – z*

A:

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: Find f if ∇f = 4xy i + (2x^2 + 8y) j

A: Here I am attaching image so that you understand each and every step.

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

A:

Q: What do you call the required function in the process of integration?

A: We have to answer  the name of the required function in the process of integration.