The domain of y = sec x is the set of all real numbers except the zeros or x-intercepts of y = sin x. O True O False

Q: Determine all values of x so that det(A) = 0, where A =

A: Given: The matrix A is x12x. Calculation: The determinant of the matrix x12x can be obtained as,…

Q: Which of these equations has two real roots: Select one: O a. x2-4x + 4 =0 O b. x2 - 10x + 100 = 0 O…

A:

Q: Given f(x) = – 2(x – 1)°(x + 3)°(4x + 5)°(x + 5)² List the zeroes (ex. 4, 6, -2): Degree: End…

A:

Q: Use interval notation to represent all values of x satisfying the given conditions: y = 1 - (x + 3)…

A:

Q: Find two positive real numbers x and y such that they add to 120and x 2y is as large as possible.

A: Given: x+y=120and  y=120-xAlso given that z=x2ybut we have z=x2120-x=120x2-x3    ...(1)

Q: a. Prove that ex>= 1 + x if x>= 0. b. Use the result in part (a) to show that ex>= 1 + x +…

A:

Q: Use interval notation to represent all values of x satisfying the given condition. y = 1 - (x + 3) +…

A: y=1-x+3+2xy is atleast 4 i.ey≥41-x+3+2x≥41-x-3+2x≥4

Q: (c) Prove that the equation x + 5x = 4cos.x cannot have more than one real root.

A:

Q: Find all solutions of the equation in the interval [0, 27). (Enter your answers as a comma-separated…

A:

Q: Find real numbers x and y such that ty 2 2 - i i+3 1 +1

A:

Q: For all real numbers x, cos (2x)= (a) 2 sin x cos x2 sin x cos x (b) sin (x2)sin x2…

A: SOLUTION- formulaconsider the addition formulacos (A+B)=cos A cos B-sin A sin B

Q: If n is any real number and f(x) = x", then f'(x) = nx"-!

A: Why does ddxxn=nxn-1                 ddxfx=limh→0fx+h-fxh…

Q: The interval ___________ consists of all real numbers for which x ≤ a.

A:

Q: Let c be a real constant. Show that the equation x – 15x + c = 0 has at most one real root in the…

A: Rolle’s theorem states that if a function f is continuous on the closed interval [a, b] and…

Q: Which of these equations has two real roots: Select one: O a x2 - 4x + 4 =0 O b. x2 - 10x + 100 = 0…

A:

Q: For all real numbers x and y, [x]+ [y] = [x + y] – 1. For all real numbers x, [x –1] = [x] – 1. | -

A:

Q: Let the domain of x be the set of negative real numbers. Then Vx, (1+ x² > 0) is a true statement a…

A:

Q: Letx, y, and z be positive real numbers. Show that: xyz(x+ y+z)sr°y+ y°z+z°x

A:

Q: if f (x) 9-x and g (x) = Vx, then the domain of (gof) (x) is: [-3,3] O [0, co0) O (-00, c0) O (-0,…

A: on solving this we get

Q: Show that [x+y] ≥ [x]+[y] for all real numbers x and y.

A:

Q: I. Solve using De Moivre's Theorem. 1. Find the real values of x and y such that (x + y)³ is greater…

A: We need to find the values of x and y, such that (x + y)3 is greater than 8.  Let us take x =…

Q: Show that x - c is not a factor of f (x)for anyreal number c.

A: We have given fx=-x4-3x2-2 We can see here fx<0 for all x belong to set of real numbers. If x-c…

Q: express the set of numbers x satisfying the given condition as an interval.       I 3x + 5 I < 1

A: To solve the inequality: 3x+5<1 Solution: We know that if x<a then -a<x<a. We have…

Q: If F (x) = | Vidt for all real numbers x > 0, then F'(x) = A в X D) 2x2

A: Given function is                                F(x)=∫4x2tdt we have to find derivative of F, we…

Q: 3x こ

A: Exponential equation: - The bases on both sides of an exponential equation may or may not be the…

Q: how do i find the coordinates of the zeros of f(x) for x e [0 , 2π]? f(x)=3sin2(x-π/3)

A: General solution of sin(x) = 0 is     x = nπ where, n = 0,1,2,3......

Q: Let c be a real constant. Show that the equation x – 15x +c=0 has at most one real root in the…

A: Our Aim is to show that the equation x3-15x+c=0 has at most one real root in the interval -2,2.

Q: The domain of f(x) = cos-(x) is: O all real numbers [- π/2, π/2] O -1. 1]

A: givenf(x)=cos-1(x)all values of x for which f(x) is valid is called domain.

Q: Determine the interval(s) on which x² + 2x-3 > 0. O a) x>1 b) -3 1

A: We want to find the interval which satisfy given inequality.

Q: Discrete

A:

Q: x-4 f(x) = In %3D x² – 5x + 6)

A: Given:  f(x)= ln x-4x2-5x+6⇒ f(x) =…

Q: a? - 1 x² + 2x+- at -5' x+2 ;x>0 Let f(x) = { Find all possible real values of a such that f(x)…

A:

Q: If plq-r)x+q (-p)x+rp-q) = 0 has equal roots, then prove that ² = 1,1 9 Pr pr

A:

Q: If x is any real number, then cosh x = Σ + Σ n! n=0 n! n=0

A: We have to find out

Q: The function f(x) = 4 for x < 2 and f(x) = 4 for x 2 2 has domain of all the real numbers. To True O…

A: As we know that domain is all the value of input (x-values) for which a function can define. for…

Q: Let f(x)=x^2-6x+9. Find x such that f(x)=1 The solutions are nothing

A: First I have set the polynomial equal to 1  That is set,  f(x)=1 and solve for x, we get x=2, X=4

Q: If an inflection point of the aurve f(x)=acos(2.x) +bsin(3x) is P(z/6,5), then what are the real…

A: At inflection point :   d2dx2fx=0d2dx2acos2x+bsin3x=04acos2x+9bsin3x=0

Q: {x|x is all real numbers}

A: Given: {x|x is all real numbers}

Q: Which of the following is not in the domain of sec(x)? Select all correct answers. Select all that…

A: The domain of the function y=sec(x)=1cos(x) is again all real numbers except the values where cos(x)…

Q: • The domain of f(x) 3-х is 1-x2 1. R 2. R/{1,-1} 3. R/{3} 4. (0, co)

A: Domain: The domain of the function is defined as the set of all input values for which the function…

Q: Find the roots of the function f(æ) = (2" – 1) · (x² + 2x – 3) with x € R.

A: To find→Roots of f(x)=(2x−1)⋅(x2+2x−3),x∈ℝ.Solution→Solving…

Q: (a) State the Intermediate Value Theorem and use it to show that y = r +x +1 has exactly one real…

A:

Q: For all real numbers x, what is the maximum value of 5 sin 2x? A. 1 BO 10 2(pi)/5

A:

Q: Find all values of x in the interval [0,2pi) 2sin^2x+5sinx-3=0

A: Given equation is, 2sin2x+5sin x -3=0

Q: Find the Domain of fif f(x) = 2(x – 7)2 Domain: > 0 O Domain: y >0 Domain: x is all real numbers O…

A: Explanation of the answer is as follows

Q: Solve and show that which of the following are analytic and non-analytic. x- iy 2 x* + y

A:

Q: 1. ƒ : R → R, such that f(x) = 10 - 3x. 2. f: ƒ : R_ → R, such that f(x) = x - 2. Here, R denotes…

A: Given: The two-real valued functions, 1. f:ℝ→ℝ, such that f(x)=10-34x. 2. f:ℝ_→ℝ, such that…

Q: Let x be a real number. Show that 1 [3x] = [x] + | x + - 3 3 ++1+

A:

Q: Find the value of x if the matnx 1 5] 4 is Singular 2. A = -3 6. 2

A:

Q: Find (fo g)(x) and (g o )(x). Also specify the domain for each. f(x) = , g(x) = 4x + 5 %3D %3D (fo…

A: