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Question: Find the general solution of the differential equation y\'\' - 5y\' + 6y = 0.Options: y = ..
Question: Solve the differential equation y\' = 3y + 6.Options: y = Ce^(3x) - 2y = Ce^(3x) + 2y = 2e..
Question: What is the solution to the first-order linear differential equation dy/dx + y = e^x?Optio..
Question: Find the particular solution of dy/dx = 2x with the initial condition y(0) = 1.Options: y ..
Question: Solve the differential equation y\'\' + 4y = 0.Options: y = C1 cos(2x) + C2 sin(2x)y = C1 ..
Question: What is the solution to the differential equation dy/dx = 2y + 3?Options: y = Ce^(2x) - 3/..
Question: Find the general solution of the differential equation dy/dx = y.Options: y = Ce^xy = Ce^(..
Question: Solve the differential equation dy/dx = 3x^2.Options: y = x^3 + Cy = 3x^3 + Cy = x^2 + Cy ..
Question: What is the derivative of f(x) = ln(x^2 + 1) at x = 0?Options: 012undefinedCorrect Answer:..
Question: For the function f(x) = x^2 + kx + 1 to be differentiable at x = -1, what must k be?Option..
Question: Is the function f(x) = x^3 - 3x + 2 differentiable at x = 1?Options: YesNoOnly left differ..
Question: Find the derivative of f(x) = e^x * sin(x) at x = 0.Options: 10esin(0)Correct Answer: 1Sol..
Question: The function f(x) = { x^2, x < 1; 2x - 1, x ≥ 1 } is differentiable at x = 1 if which cond..
Question: For which value of a is the function f(x) = x^2 - ax + 2 differentiable at x = 1?Options: ..
Question: If f(x) = x^2 sin(1/x) for x ≠ 0 and f(0) = 0, is f differentiable at x = 0?Options: YesNo..
Question: Determine the point at which the function f(x) = |x^2 - 4| is differentiable.Options: x = ..
Question: Find the value of k for which the function f(x) = x^3 - 3kx^2 + 3k^2x - k^3 is differentia..
Question: What is the derivative of f(x) = x^5?Options: 5x^44x^5x^45x^3Correct Answer: 5x^4Solution:..
Question: Calculate the derivative of f(x) = x^2 * e^x.Options: (2x + x^2)e^x2xe^xx^2e^x(x^2 + 2x)e^..
Question: What is the derivative of f(x) = 5x^4 - 3x + 2?Options: 20x^3 - 320x^3 + 315x^3 - 35x^3 - ..
Question: Find the derivative of f(x) = tan(x).Options: sec^2(x)csc^2(x)sin^2(x)cos^2(x)Correct Answ..
Question: What is the derivative of f(x) = x^3 - 4x^2 + 6x?Options: 3x^2 - 8x + 63x^2 + 8x + 62x^2 -..
Question: Find the derivative of f(x) = ln(x^2 + 1).Options: 2x/(x^2 + 1)1/(x^2 + 1)2/(x^2 + 1)x/(x^..
Question: Calculate the derivative of f(x) = e^(2x).Options: 2e^(2x)e^(2x)2xe^(2x)e^(x)Correct Answe..
Question: Calculate ∫ from 0 to 1 of (x^2 + 1/x^2) dx.Options: 1234Correct Answer: 3Solution: The in..
Question: Evaluate ∫ from 1 to 3 of (2x + 1) dx.Options: 8101214Correct Answer: 10Solution: The inte..
Question: Calculate ∫ from 0 to 1 of (1 - x^2) dx.Options: 1/31/22/31Correct Answer: 1/2Solution: Th..
Question: Find the value of ∫ from 0 to 1 of (x^3 - 3x^2 + 3x) dx.Options: 0123Correct Answer: 1Solu..
Question: Evaluate the integral ∫ from 0 to 1 of e^x dx.Options: e - 1e10Correct Answer: e - 1Soluti..
Question: Calculate ∫ from 0 to π/2 of sin^2(x) dx.Options: π/4π/2π/3π/6Correct Answer: π/4Solution:..
