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Question: Evaluate the limit: lim(x->infinity) (2x^3 - 3x)/(4x^3 + 5)Options: 1/201InfinityCorrect A..
Question: Find the limit: lim(x->0) (tan(3x)/x)Options: 301InfinityCorrect Answer: 3Solution: Using ..
Question: Evaluate the limit: lim(x->infinity) (3x^2 + 2)/(5x^2 - 4)Options: 3/501InfinityCorrect An..
Question: If f(x) = |x|, is f differentiable at x = 0?Options: YesNoOnly from the rightOnly from the..
Question: For the function f(x) = x^3 - 3x^2 + 2, find the points where it is not differentiable.Opt..
Question: Is the function f(x) = x^2 - 4x + 4 differentiable everywhere?Options: YesNoOnly at x = 0O..
Question: For which value of a is the function f(x) = x^3 - 3ax + 2 differentiable at x = 1?Options:..
Question: The function f(x) = sqrt(x) is differentiable at x = 0?Options: YesNoOnly from the rightOn..
Question: For the function f(x) = x^2 + 2x + 1, what is f\'(x)?Options: 2x + 12x + 22xx + 1Correct A..
Question: If f(x) = x^3 - 3x^2 + 4, then f\'(1) is equal to?Options: 1234Correct Answer: 2Solution: ..
Question: Find the value of ∫ from 0 to 1 of (x^3 - 4x + 4) dx.Options: 0123Correct Answer: 1Solutio..
Question: Evaluate ∫ from 0 to 1 of (x^2 + 3x + 2) dx.Options: 1234Correct Answer: 3Solution: The in..
Question: Calculate ∫ from 0 to 1 of (x^4 - 2x^2 + 1) dx.Options: 011/32/3Correct Answer: 2/3Solutio..
Question: Find the value of ∫ from 0 to 1 of (e^x) dx.Options: e - 11e0Correct Answer: e - 1Solution..
Question: Evaluate ∫ from 0 to 1 of (4x^3 - 3x^2 + 2) dx.Options: 1234Correct Answer: 3Solution: The..
Question: Calculate ∫ from 0 to π/2 of sin(x) cos(x) dx.Options: 1/21π/4π/2Correct Answer: 1/2Soluti..
Question: Find the value of ∫ from 1 to 2 of (3x^2 - 2) dx.Options: 1234Correct Answer: 1Solution: T..
Question: Find the value of ∫_0^1 (1 - x^2) dx.Options: 1/31/22/31Correct Answer: 1/2Solution: The i..
Question: Calculate ∫_0^1 (x^3 - 2x^2 + x) dx.Options: -1/1201/121/6Correct Answer: 1/12Solution: Th..
Question: Evaluate ∫_1^3 (2x + 1) dx.Options: 8101214Correct Answer: 10Solution: The integral evalua..
Question: Find the value of ∫_0^π/2 cos^2(x) dx.Options: π/4π/210Correct Answer: π/4Solution: The in..
Question: Evaluate ∫_0^1 (x^4) dx.Options: 1/51/41/31/2Correct Answer: 1/5Solution: The integral eva..
Question: Evaluate ∫_1^2 (3x^2 - 4) dx.Options: 1234Correct Answer: 1Solution: The integral evaluate..
Question: Which of the following functions is not continuous at x = 1?Options: f(x) = x^2f(x) = 1/xf..
Question: The function f(x) = { x^2, x < 0; 1, x = 0; x + 1, x > 0 } is continuous at x = 0?Options:..
Question: For which value of a is the function f(x) = { x^2 + a, x < 1; 3, x >= 1 } continuous at x ..
Question: The function f(x) = { 1/x, x != 0; 0, x = 0 } is continuous at x = 0?Options: YesNoOnly fr..
Question: If f(x) = { x^2, x < 3; k, x = 3; 2x, x > 3 } is continuous at x = 3, what is the value of..
Question: The function f(x) = { x^2, x < 1; 2x - 1, x >= 1 } is continuous at which point?Options: x..
Question: If f(x) = e^x - x^2, find the x-coordinate of the local maximum.Options: 0123Correct Answe..