Mathematics for Engineering

# Quiz Exercise 1.

Calculate:

Exercise 2.

Calculate:

Exercise 3.

Find all a values for the equality: $-5+i+\left(2+a{\right)}^{2}$ where a is an imaginary number.

Exercise 4.

Resolve the system of equations:

Exercise 5.

Find all the complex numbers z for the following statements:

Exercise 6.

Show the unity of points z on the complex plane what correspond to an inequity |z-2i+1|≤5.

Exercise 7.

Represent the complex number z=√3 i-1 with its trigonometric form.

Exercise 8.

Find the following derivatives using sum, residual, composition formula for the functions:

• tan ⁡x;
• cot ⁡x;
• sinh ⁡x;
• cosh ⁡x.

Exercise 9.

Find derivative of function in the point x.

a. y=√x, x=4
b. y=x*|x|, x=0

Exercise 10.

Find derivatives and differentials for the functions below:

Exercise 11.

Find derivatives and differentials for the functions below:

Exercise 12.

Find differentials for the following functions:

Exercise 13.

Find differentials of the functions using theorem of inverse function derivative:

Exercise 14.

Calculate the integrals:

Exercise 15.

Calculate the integrals:

Exercise 16.

Calculate the integrals:

Exercise 17.

Calculate the integrals:

Exercise 18.

Calculate the integrals:

Exercise 19.

Calculate the integrals:

Exercise 20.

Calculate the derivatives for functions below:

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