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Question: The function f(x) = x^2 + 2x + 1 is differentiable everywhere?Options: TrueFalseOnly at x ..
Question: The function f(x) = |x| is differentiable at x = 0?Options: YesNoOnly from the rightOnly f..
Question: If f(x) = x^3 - 3x^2 + 4, then f\'(2) is equal to?Options: 0123Correct Answer: 1Solution: ..
Question: Which of the following is a characteristic of alkenes?Options: Single bonds onlyAt least o..
Question: If f(x) = 5x^2 + 3x, what is f\'(1)?Options: 8101315Correct Answer: 10Solution: f\'(x) = 1..
Question: What is the derivative of f(x) = x^4?Options: 4x^33x^42x^4x^3Correct Answer: 4x^3Solution:..
Question: Find the derivative of f(x) = tan(x) at x = 0.Options: 01undefined1/2Correct Answer: 1Solu..
Question: What is the derivative of f(x) = 3x^3 - 5x + 2?Options: 9x^2 - 53x^2 - 59x^2 + 53x^2 + 5Co..
Question: If f(x) = ln(x), what is f\'(x)?Options: 1/xxln(x)0Correct Answer: 1/xSolution: f\'(x) = 1..
Question: What is the derivative of f(x) = e^x?Options: e^xx*e^x10Correct Answer: e^xSolution: The d..
Question: Find the derivative of f(x) = sin(x) at x = π/2.Options: 01-1undefinedCorrect Answer: 1Sol..
Question: What is the derivative of f(x) = x^2 at x = 3?Options: 36912Correct Answer: 6Solution: f\'..
Question: Evaluate ∫_0^1 (x^3 + 2x^2) dx.Options: 1/41/31/21Correct Answer: 1/2Solution: ∫_0^1 (x^3 ..
Question: Calculate ∫_1^e (ln(x)) dx.Options: 1e - 1e0Correct Answer: e - 1Solution: ∫_1^e ln(x) dx ..
Question: Evaluate the integral ∫_0^π/2 cos^2(x) dx.Options: π/4π/210Correct Answer: π/4Solution: ∫_..
Question: Find the value of ∫_0^1 (x^4) dx.Options: 1/51/41/31/2Correct Answer: 1/5Solution: ∫_0^1 x..
Question: Evaluate ∫_0^1 (e^x) dx.Options: e - 1e10Correct Answer: e - 1Solution: ∫_0^1 e^x dx = [e^..
Question: Calculate ∫_0^1 (4x^3 - 3x^2 + 2) dx.Options: 1234Correct Answer: 2Solution: ∫_0^1 (4x^3 -..
Question: Evaluate the integral ∫_1^2 (3x^2 - 2) dx.Options: 1234Correct Answer: 1Solution: ∫_1^2 (3..
Question: Find the value of ∫_0^π sin(x) dx.Options: 0123Correct Answer: 2Solution: ∫_0^π sin(x) dx ..
Question: Evaluate the integral ∫_0^1 (x^2 + 2x) dx.Options: 1234Correct Answer: 2Solution: ∫_0^1 (x..
Question: Which of the following is a necessary condition for a function to be continuous at a point..
Question: For the function f(x) = { x^2, x < 1; 3, x = 1; 2x, x > 1 }, what is the value of f(1)?Opt..
Question: Which of the following functions is not continuous at x = 0?Options: f(x) = x^3f(x) = e^xf..
Question: If f(x) is continuous on [a, b], which of the following must be true?Options: f(a) = f(b)f..
Question: What is the limit of f(x) = 1/x as x approaches 0 from the right?Options: 0Infinity1Does n..
Question: The function f(x) = { 3x + 1, x < 1; 2, x = 1; x^2, x > 1 } is continuous at x = 1 if whic..
Question: Which of the following statements is true about continuous functions?Options: They can be ..
Question: If f(x) = { x^2 + 1, x < 0; k, x = 0; 2x + 1, x > 0 }, what value of k makes f continuous ..
Question: Determine the continuity of the function f(x) = { x^2, x < 1; 2x - 1, x >= 1 } at x = 1.Op..
