15. Show that the equation, 2³ + e* = 0 has exactly one real root.

Q: Show that there is a root of the equation x3 - x - 1 = 0 between 1 and 2.

A: Consider the given equation. x3-x-1=0 and, fx=x3-x-1 Put x=1 in the function. f1=13-1-1=-1

Q: 1.4.2 y(r)= Mar(1- r|,0) %3D to show this function is not a positive definite function we use…

A: We will find the values of x1,x2,x3 and c1,c2,c3.

Q: Exercise(6): (1) Solve the following Cauchy-Euler differential equations: (a) 4r y" +4.ry-y = 0.

A: Solution:

Q: Let A = (-0,0), B=(0,0) then AUB=

A:

Q: Q2. Find the solution of the following cquations. i) 3(7 +5) - 27 ii) log, r - 2 - log, (a - 8)

A: Use logarithmic property:-

Q: Obtain all four roots of the equation = ++-0, and then express * +4 as product of quadratic factors…

A:

Q: ] Prove that the equation 2" – x = 1+ 4/x has a solution greater than 0.

A:

Q: 2.4 If (1 p) is a root of quadratic equation - x+px + (1 - p) = 0, then find its roots.

A:

Q: e) Solve [(-x'y)² + (x²y)³]²

A:

Q: Solve 2zx-px²-2qxy+ pq=0.

A:

Q: 11. Show that 1 + 4i is a root of the equation 2z3 - 3z2 + 32z + 17 = 0. Hence, find all the roots…

A: Answer

Q: cosh“ x – sinh“ x = (cosh? x – sinh? x) (cosh² x + sinh² x)

A:

Q: h-x, k-у, _а(h — x,)+Ы(k - у,) a? +b? a b

A:

Q: 6). Solve xdy- yk -0 x +y* xdx + ydy +-

A:

Q: 2 X 2 X 0+ - 4 +4 dx =

A: C+C

Q: Gym Workout 24 Your Gym Ultra Club Fees $200 plus $55 per month $50 plus $60 per month $20 plus $65…

A: Given, a table which represents a different type of Gym and their fees respectively.It is required…

Q: Solve for x. 5 12х — 7 - х — 7 x + 4 x2 – 3x — 28 - - - ||

A:

Q: (1) Solve the following Cauchy-Euler differential equations: (a) 4r y"+4ry - y = 0.

A:

Q: yV – y" + 2y' = 0. %3D

A: Topic = Differential equation

Q: Now solve for x. 1+ 8y = x(5 - 2y) 1 + X =

A:

Q: Use the intermediate value theorem to prove that the equation 3 solution. = T has at least one real

A: If the value of the function f(x) has opposite signs [f(a)>0&f(b)<0 or…

Q: 6. Express the roots of the equation x + 1 = 8(x- 3) in a+ bi form.

A:

Q: Show that there is a root of the equation x³-4x² +1=0 between 0 and 1

A:

Q: Solve exactly for ( 0, 2π)

A: Simplifying the given equation:Using the zero product rule: