C. Show that f(x) = (x26)² has no inverse on the interval (-∞,0).

Q: Sketch the domain of the f(x, y) = ln((x² + x² – 4)(16 – x² – y²)) |

A: Recall:  Domain of the function:           The domain of the function is the set of all values for…

Q: Let f(x) = V5x + 4. Compute (f-1)'(2) using the Derivative of an Inverse Function Theorem.

A: Solution

Q: Z→ Z be such that f(x) = 4x + 2. Is f invertible, and if so, find its inverse function.

A: Given query is to find the inverse function.

Q: What is derivation of f(x) = (2x² – x + 1)³ at %3D Xo = 1 ?

A:

Q: Find the linearization L(x) of the function f(x) = x^3/4 at x=256.  L(x)=?

A:

Q: Express f(z) = x-1-iy (x−1)² + y² in terms of z.

A:

Q: Let f(x)= x2 − 6. Prove that the root of this function is equal to √6 {correct to 2 dp}, and lays…

A:

Q: Prove that for all a, b = R, the function f(x) = 3x² - 4x³ + 6x² + ax + b has exactly one point…

A:

Q: Ex/ show that f(x) = x+7x + 4 x + 1 has an inverse. %3D

A: In this question we have to find whether the function has an inverse.

Q: fG)=4x-3 SC) = (f of ) (x)=

A: Given fx=4x-3.

Q: Q1. Find ý of the function x2 – e2x+3y – In(xy³) = 0. -

A: here is the solution

Q: Find f(1) if f(t) dt = x- x + 2x2- 2, x >1. %3D

A: Given, ∫1x2ftdt = x6 -x4  +2x2 -2               x≥1 We have to find   f1

Q: b- Determine the critical point of the function f(x) = x5 – 5x* + 5x³ –- 1 %3D

A:

Q: Use the intermediate value theorem to show that f(x) = x^4 + 8x^3 −x^2 + 2 has a zero in I = [−1,…

A: Given,

Q: 2. Calculate the point(s) of intersection of f(x) = 2x² + 4x – 11 and g(x) = -3x + 4.

A: Given f(x) = 2x2 + 4x - 11 and g(x) = -3x + 4

Q: D. Discuss the continuity of the function g (x): 1 %3D on the interval [-1,2]. x2-4

A: Given, To discuss continuity of the function g(x)

Q: Find (f-)'(a). f(x) = 4 + x2 + tan(Tx/2), -1 < x < 1, a = 4 %3D (F-1)'(a) =

A:

Q: Find the linearization of f(x) =2x² + 4x – 3 at x= -1

A:

Q: Find the linear approximation of f(x) = x4 + 3x2 at a = 1.

A: We first find f'(a)=f'(1) f(x)=x4+3x2f'(x)=4x3+6xf'(1)=4(1)3+6(1)f'(1)=4+6=10   We now find f(1).…

Q: If a F (2) = xy+i (x² – y²), what is F (-1+2i)?

A: given  F(z)=xy+i(x2-y2) To find the value of  F(-1+2i)

Q: (B) The function f(x) = x² + x +1 has no fixed point, prove that.

A: Let X be a nonempty set and f : X → X. A point x ∈ X is a fixed point of  f, if f(x) =x.  If no…

Q: Show that f (x) = 2x − 18 is invertible. What are the domain and range of f−1?

A: Given: f(x)=2x-18

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f(x) x - 1

A: To show the f(x) has roots between a and b we have to show that

Q: Obtain the ROOT of the f(x)=x²-2e-×+e-2x function using

A: b. Newton Rapshon method  fx=x2-2e-x+e-2x f'x=2x+2e-x-2e-2x , x0=4 1st iteration…

Q: Show that f(x1, x2) = 2 - (x1 - 1)^2 - e^x2^2 is concave.

A: the given function is fx1,x2=2-x1-12-ex22 To find the function is concave we have to show all its…

Q: The function f(x) = x²e*- ex has a root in [0,2]

A:

Q: Find the best quadratic approximation to f on the interval [ 0, 1].                     f(x) = x3

A:

Q: Find the positive critical point of the function f (x) %3D x4 + 7 x =

A:

Q: 5. Show that the function f (x) has roots between (0,2) x + 2x – 3 f(x) = %3D x – 1

A: Given that: f(x)=x2+2x-3x-1

Q: The function f(x) =x -x² – 2x – 1 is increasing over: %3D

A:

Q: Find the value k that makes the function continuous. kx + 14, х > 2 f (x) = 11x + 2, x < 2

A:

Q: . The function f(x, y)= 8x' - /4x* + 3y* is homogenous in x and y of degree -. The function f(x, y)=…

A: Here we have to find the degree of homogeneous function

Q: The domain of the function f (x, y) = In(2 – /x² + y² ) is:

A:

Q: DERIVE THE F. FUNCTIONS: s) y (x-3)(3x+4)(x²-2x+ 1)

A:

Q: Explain why g(x) = f(x), if x ≤2 0, if x > 2 is not differentiable at x = 2.

A:

Q: The function f(x) 223 42x? + 240x – 11 has two critical numbers. The smaller one is x = and the…

A: Let's find.

Q: Find the Critical number of the function f(x) = -2x^2 + 16x + 7. x = ?

A:

Q: Find the linearization L(x) of f (x)=- Vx -5 at a =3. – 5 2.

A:

Q: Find a and b so that the function 2.3 – 5x² + 2, x -2 f(x) = ax + b, is both continuous and…

A:

Q: 5. Show that the function f (x) has roots between (0,2) x² + 2x – 3 f (x) = X - 1

A: Given that

Q: Find f for the function z = - 3x6 0 02-30x4 ex ax = ex 7x8 1 8 6x 02-02-63 x = 6xy + 4y2.

A: This question can be solved using the concept of partial derivatives.

Q: Find the linearization at x = a. 1 f(x) = = 5 +3

A:

Q: Examine whether or not the function fx' - 2r +1 ifxs 2 S (x)= x'-2r +1 [3x-2 if x>2 Is continuous at…

A: Given function, fx=x3-2x+1,     if x≤23x-2,            if x&gt;2 To find the continuity of the…

Q: The derivative of f(x) 4 (22 +17x) is O -4c (2a + 17) O -4r 2(2x + 17) O 4x + 68 O 4x 2(2x + 17) O 4

A: Here, it is given that f(x)=4x(x2+17x) We need to find the derivative of the function f(x).

Q: The function f(x) = 2x + 6x² – 5x + 1 is concave downward on the interval None (-0, –1) (-0, c0)…

A: Concavity.

Q: Let f(x, y) = -e2"-y + In(3x – y). Find the domain of this function.

A:

Q: The function f(x) = x³ – 3x² + 5 is concave upward on the interval O (-∞, 1) (1, co) (-∞0, ∞0) O…

A: