Show that the equation 2x+ sinx=0 has exactly one real root. (Hint: Step 1 show that the equation has at least one real root. Step 2 show that the equation has at most one real root.)

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A: Given problem:-

Q: lim(10) 1. A. 11 B. 10 D lim(x² 2. 3x 1) A. 11 B 10 D. 25 3. lim A. 18 B. 17 C. 16 D. 15

A: Solving the problem by finding the value of the limit.   NOTE :: As per our Expert guidelines we are…

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A: I am attaching image so that you understand each and every step.

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Q: 3 | (16t3 – 12t? + 6)dt

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Q: Evaluate the Following limts 9-X VX-3

A: We can evaluate the limit as below.

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A: Given query is to find the Indicated integral.

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A: Given query is to find the solution of the expression.

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A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

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A: Given query is to find the derivative of the expression.

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Q: Evaluak the following limits 9-x VX-3

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A: Topic = Trigonometry

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A: The given region is bounded by: x2+y2=4,y=x,y=x3

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A: We can answer the question as below.

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A: Given problem:-

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A: The curve is y=xx, whose tangent line is parallel to y=6+3x

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A: To find out the length of the two pieces.

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Q: 12 10 12 | f(æ) dæ = 9, | f(x) da = 14, | f(x) dz = 5. Suppoe 6. 11 Then 11 | f(x) dx = Σ %3D 10 10…

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