Exercise 2. Find the general integral of 1"- (2+a)r' +2ar-4 0 in dependence of a e R, a 2. Are there values of a 2 such that any solution of the differential equation posses an horizontal asymptote as t → -o0? Exercise 3. Given the function of two variables f(r, y) = x" find its domain. Then, find the equation of the tangent plane at (1,2, f(1,2)).

Q: 8. y=x(x+5)(x-8)

A: We can find the answer as below

Q: Write the following statements in function notation. Determine the independent and dependent ` The…

A: A function notation is nothing but writing the dependent variable as a function of the independent…

Q: 1. Find the function y(t) satisfying y' = ev-t(1+t?) sec y with y(0) = 0.

A: Claim: solution for with y(0)=0. Integrating both sides we get, Take u=e-y then du=-e-y  and…

Q: each function b) graph each x 9. y=(x+1)(x- 3)(x-8)

A: To graph the equation.

Q: Find Maclaurin function of fız)- the Z-7 5-22-2

A: We have to solve given problem:

Q: for - 1<x<1. Prove that for the inverse cosine function, (cos- x) = dx 1-x

A: Here, the objective is to prove the following:  ddxcos-1x=-11-x2   -1&lt;x&lt;1

Q: What are the expressions simplified and are the functionsinverses?

A: We will show that, both f°h and h°f are identity maps on their respective domain. Then, we can claim…

Q: Evaluate Function  g(3,4) when g(x,y)=x-6y/x^2+y^2 a. -25/21 b. -5/21 c. -21/25 d. -21/5

A: For this problem, we have to substitute the values of x and y in given function g(x,y).

Q: 1s the ordered pairs a tuncrion? {(3,4)(-3,4)(6,-2)(-2,3)(2,7)(5,4)} a function?

A: We have to check

Q: Refer to the function f = {(-2, 4), (9, 6), (2, 7), (7, 9)}. Determine f(-2). f(-2)=1 X

A:

Q: Determine if each represents a func {(1, 1), (2, 2), (3, 5), (4, 10), (5, 15)}

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: GIven the function fa)= (1t2x), compute f1). Round to nearest tenth.

A:

Q: Write a function rule for the area of a rectangle with a length 2 ft less than three times its with.…

A: Let,width =  ftlength =  ftlength is 2 ft less than three times its with. ......(i)

Q: F(r) = 5x sin(/2x) – 3 cos(/2x) +xe³r sin(3x) + 2x ?

A:

Q: Determine whether the function {(0, - 4), (2, - 2), (4, 0),(6, 2)} is one-to-one

A: Given: Let fx=0, -4, 2, -2, 4, 0, 6, 2 To Find:  To determine whether the given function is…

Q: Find Greens function for: d?y – a²y = f(x) dx? where a is a constant subject to boundaries: y(0) =…

A:

Q: 15. Input, 1 3 4 Output, y -3 -6 -9 -12

A:

Q: Let f=​{(0​,8​),(5​,0​),(9​,4​)}. Find f(0)

A: We have given f.  We have to find f(0)

Q: Which . functions are continuous through its domain?

A: Continuous Function: A function fx is continuous at a point c of its domain if  limx→cfx=fc A…

Q: (6,12), (3,1), (-1,13),(6,4) is this represent a function

A:

Q: define convolution of two functions?

A:

Q: Evaluate the function 4" when x = {1, 2, 3, 4, 5}. x input y output 1 2 3 4

A: A

Q: Which of the following are functions? Explain how you know for each. a/ {(2, 3), (3, 2), (2, 5)},…

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.