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Q: 4. a) For 0≤x≤ 1, show that < x² √1+x < x² b) Use the estimate in a) and integrate it to prove that…

A: We have to prove given inequalities.

Q: Find all of the solutions of the equation on the interval [0, 2n]: secxcscx=2cscx. ○ 풀, 풍, 0, n, 2m…

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Q: A parallelogram is formed by the vectors a = (1, 0, -1) and b = (2, 1, 1). What is the area of the…

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Q: stly cloudy F1 How many solutions does the following equation have on the interval [0, 271? 2sin220…

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Q: Suppose that sec() = 5, tan() < 0. Compute the six trigonometric functions at the angle 9. cos(8) =…

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Q: Use the function and the accompanying figure to answer the following questions. a. Is f defined at x…

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Q: 10. Determine dy of y = 5-2x+7 dx In 5 -2(5-²x+7) ○ (5-2x+7) In 2 ○ (5-²*+7) In 5 ○ 2(5-2x+7) In 2

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Q: Use implicit differentiation to find an equation of the tangent line to the curve sin(x + y) = 4x -…

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Q: f(x) and g(x) are continuous functions. f(x) f'(x) g(x) g'(x) -3 3 -4 5 4 -1 -3 -2 -1 2 1 5 -1 1 2 3…

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Q: Find the angle between the vectors, approximate your answer to the nearest tenth: v-(-3,-2), w=…

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Q: Use the Law of Cosines to solve for the largest angle in the triangle with the given measures. Round…

A: The largest angle in a triangle is opposite to the largest side of the triangle.In a triangle with…

Q: If f(1) = -3 and f'(x) ≥ 5 for x = [1, 5], what is the smallest value f(5) can possibly be? Bug…

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Q: Find all of the solutions of the equation on the interval [0, 2n]: tan²xsinx = sinx. O 0, п, 2n

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Q: 3. Find an equation for the tangent line at the given point. x+x²) ¹⁰, y = (1 + x + (0, 1)

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Q: Rationalize the following denominator: √5-3√3 √6 3√10-6√2 6 O√30-6√2 3 3√10+3√2 6 √30+9√2 6

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Q: Let f (x) y=x+4 y=x y=x+2 y=x-2 x²-x+4 x-3 . what is the equation of the oblique asymptote of f(x)?

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 14. a. As x→→∞, f(x) → c. As x→-3˚, f(x) → e. The graph is increasing over the interval(s) g. The…

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Q: Determine the solution to the following system of equations: (3) 1 HUNGA 11 ++ I 1-63-62-6 b b b ++…

A: First we eliminate z from this system of equations.

Q: Find the intervals on which f is increasing and decreasing. f(x) = -x² +2 Inx

A: the given function   for increasing or decreasing we have to find the first order derivative By the…

Q: Given the following piecewise function, evaluate f(4). Do not include "f(4) =" in your answer. [ 5x…

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Q: d(x) = [-x-k, if x = -1 2x+ 2k, if x = -1 k = 1 نی =-4 k=-1 k = 0 Determine k so that (x) is…

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Q: Use the Divergence Theorem to evaluate / F. ds where and S is the boundary of the sphere x² + y² +…

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Q: Find r(t) if r'(t) = t² i + et j + 3te³t k and r(0) = i + j + k. r(t) =

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Q: Find the critical points/numbers as well as the extrema of the given function.( 3 f(x) = 3x² + 4x³ -…

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Q: why was in step 2 the denominator is t-2 then in step 3 it became t-4?

A: To evaluate the following integral.Note: After seeing the previous solution, we observe that there…

Q: 5. Seven drugs were tested for diabetic patients. Two drugs are given at a time in combination one…

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Q: The graph of s = f(t) represents the position of an object moving along a line at time t≥ 0. a.…

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Q: Consider the rational function g(x) 3x²-5x-2 (i) Factorise the numerator and denominator. (ii) Find…

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Q: Match the function f(x) with its derivative f'(x) Blue-green are functions, purple are derivatives…

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Q: 5. What is the derivative of ♬(x) = (3x² + 7)³₂ ) f'(x) = 18(3x² + 7)² f'(x) = (3x² + 7)² f'(x) =…

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Q: 4 (6) Find the derivative y' for the Following function 2x 1) Y = √₂²² sin (e²-1)dt 2y=1-cos (x ²-2)…

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Q: 1) True or false: If f has minimuh at x=c, then f'(c) = 0 a local maximum or

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Q: could you please show all the work handwritten for this question

A: The solution is shown below-

Q: If u = 2i - j; v = -5i + 4j and w = j find -2u. (v + w). * Student can enter max 2000 characters…

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Q: A plane travels N45°E at an airspeed of 1000 km/h. Measurement on the ground shows that the plane is…

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Q: FOR WHAT VALUES. OF A INFLECTION OF THE CURVE AND B IS (2, -16) A POINT OF GUEN BY 3 f(x) = Ax² -…

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Q: The result of a dot product is a scalar. True O False

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Q: Consider the series Answer: L = ∞ 8 n=1 3n-11 6n +3 V 2n Evaluate the the following limit. If it is…

A: We have to check weather the given series is converse or divergent.

Q: If the profit for producing x units can be approximated by the function P(x) = 0.002x³ + 100x,…

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Q: MIA Bot 3 Find the exact value of 2sin75°cos75°. O 0-1/10 HIN F2 2 √3 HIN √3 2 O 01/10 a Q Search

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Q: Find parametric equations of the line through (-2, 1, 6) that is parallel to 2i – 4j+ k. x(t) y(t)…

A: Given point: (-2,1,6) , Parallel vector= 2i-4j+k We have to find equation of line in parametric…

Q: If y = and w=, then the projection of v onto w is: 0 O O

A: We have,      v =&lt;-5, 2&gt;      w=&lt;-1,-2&gt;

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-5, 0,…

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Q: 0) Findu'ify=" (elan(t), 1) dt

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Q: exact value of cos²() using a suitable power-reducing formula. + √2 4 1-√2 2 1+√2 2 2-√2 4

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Q: In the figure below, what is the slope of the tangent line to the function at x = -2? (2, 2) -5 -10-…

A: Note:-Since you asked multiple questions according to our policy we can solve only first question…

Q: Use a software program or a graphing utility with matrix capabilities and Cramer's Rule to solve…

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Q: -8

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Q: Find a × b if b = (–6, 9, —15) and à = (4, −6, 10) (-3,-2,0) (0,0,0) (1,-1,-1) (-24,-54,-150)

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Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for…

A: We can find the value of given integration by both trapezoid and simpson rule and compare it with…