Home / AP Calculus BC : 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables- Exam Style questions with Answer- MCQ

AP Calculus BC : 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables- Exam Style questions with Answer- MCQ

Question

If \(\frac{dy}{dx}=ysec^{2}x\)
(A)\(e^{tanx}+4 \)                       (B)\(e^{tanx}+5\)                      (C)\(5e^{tanx}\)                          (D)\(tanx+5\)                                (E)\(tanx+5e^{x}\)

Answer/Explanation

Ans:C

 

Question

If \(\frac{dy}{dx}=(1+lnx)\)y and if y = 1 when x = 1, then y =

(A)\(e^{\frac{x^2-1}{x^2}}\)

(B)\(1+lnx\)

(C)lnx

(D)\(e^{2x+xlnx-2}\)

(E)\(e^{xlnx}\)

Answer/Explanation

Ans:E

Question

If \(\frac{dy}{dt}=-2y \) and if y = 1 when t = 0, what is the value of t for which y =\( \frac{1}{2}\) ?

(A) \(-\frac{ln 2}{2}\)                    (B)\(-\frac{1}{4]\)                           (C)  \(\frac{ln 2}{2}\)                        (D) \frac{\sqrt{2}}{2}\)                          (E) ln 2

Answer/Explanation

Ans:C

This is the differential equation for exponential growth.

Question

 If \( {dx}=sinxcos^{2}x \) and if y = 0 when \(x=\frac{\pi}{2}\), what is the value of y when x = 0 ?

(A) −1                                           (B) \(-\frac{1}{3}\)                                                (C) 0                                                               (D)\(\frac{1}{3}\)                                                      (E) 1

Answer/Explanation

Ans:B

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