Generate Quiz 6968A370A7424

Since the given equation’s limit is zero, replacing x with zero yields an answer of 8/5, indicating that option B is the right one.

Substitute x with the specified limit 3, then solve as follows: (12-8)/(3+2)=4/5

Now let’s assess the limit:

Limθ→2π tan(θ/2)

θ/2 approaches π/4 as θ gets closer to π/2. The tangent function has a vertical asymptote at π/2 in the interval (0,π/2).

tan(θ/2)

Since θ/2​ approaches π/4​. ​, we have:

tan(θ/2) = tan(π/4)

where tan(π/4) = 1.

Consequently,

tan(θ/2), Lim θ→2π = 1

Thus, the appropriate choice is:

(a) 1

FUNCTION COMPOSITION AND FUNCTION INVERSE:

The right response is c) 1.

When a function f(x) has an inverse function g(x), the reciprocal of the derivative of the original function f'(x), evaluated at the corresponding point, is equal to the derivative of the inverse function g'(x).

In mathematics, g(x) is the inverse function of f(x) if f(x) = g(x). The derivative of the inverse function g'(x) is provided by:

g'(x) = 1 / f'(g(x))

In this instance, we must evaluate the derivative of the inverse function g(x) at x = 1 in order to determine the value of g'(1).

When we replace the provided data, we obtain:

g'(1) = 1 / f'(g(1))

Given that f(x) = g(x), g(1) = 1.

Therefore, g'(1) = 1 / f'(1) = 1.

Therefore, c) 1 is the right response.

The right response is b) (2x + 3)^3.

g(x) =x3 f(x)=2x+3

gof(x)=g(f(x))=g(2x+3)=(2x+3)2.

The cardinality of the set X, or the total number of elements in the set, is usually indicated by the notation ∣X∣. Considering that the number of elements in X is represented by ∿X∣. Similar to how ∣Y∣ indicates how many elements there are in Y, ∣X*Y∣ usually denotes the cardinality of the Cartesian product of X and Y, or X×Y.

The set of all possible ordered pairs (x,y) where x is from X and y is from Y is known as the Cartesian product X×Y. The formula ∣X×Y∣=∣X∣⋅∣Y∣ gives the cardinality of X×Y. Therefore, choice B is the right one.

The domain will be {3,5,7,-9} since it contains the first element of every ordered pair, as in R={(3,0),(5,1),(7,-3),(-9,0)}.