lim⁡𝑥→∞𝑥4−7𝑥+94+5𝑥+𝑥3=∞,​ x→∞lim​ 4+5x+x 3 x 4 −7x+9​ =∞,​ =A.0B.1441​ C.1D.Does not existE.4SUBMITarrow_backPREVIOUS

The given expression is a rational function and we are asked to find the limit as x approaches infinity.

The function is: (x^4 - 7x + 9) / (4 + 5x + x^3)

To find the limit of a rational function as x approaches infinity, we divide every term in the function by x to the power of the highest exponent in the denominator. In this case, the highest exponent is 4.

So, we get: [(x^4/x^4) - (7x/x^4) + (9/x^4)] / [(4/x^4) + (5x/x^4) + (x^3/x^4)]

This simplifies to: [1 - (7/x^3) + (9/x^4)] / [(4/x^4) + (5/x^3) + (1/x)]

As x approaches infinity, any term with x in the denominator approaches 0. So, the limit of the function as x approaches infinity is 1/0.

However, division by zero is undefined in mathematics. Therefore, the limit of the function as x approaches infinity does not exist. So, the answer is D. Does not exist.