1. In the following exercises, evaluate each definite integral using the Fundamental Theorem of Calculus, Part 2. (e) 2 (a) (x-3x)dx (f) x dx 99 -1 3 (b) [(x +3x-5)dx (g) [(412 – 3r ) dt 5/2 3/2 -2 3. (c) [(+2)(1-3)dt (h) dx .2 -2 3 (d) [( -9)(4-r)dt (i) 2

Q: plot the function f(x)=x*sin(x)-cos(x) to show that it has one root at the interval [0,pi/2]

A: The given function is  defined in the closed interval .We shall fill the following tabular column.…

Q: A. Evaluate the following: NO Differentiation 1. lim(x³ - 2x² + 3x-1) x->2 2 lim (4 + 3r²-2r+5)

A: To evaluate the limit of the given function

Q: Let f(x) = x² – 6x +3 with domain 0 < x < 3. Calculate (f-1)'(-2) . Note: Round to two decimal…

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Q: The trigonometric substitution x - 2 = 3 sec could be useful in integrating a function (i.e., an…

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Q: In deriving three point formulas, we use Lagrange polynomial. The derivative of L1 at Xo is: Select…

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Q: Suppose f(x) =xsec²(x²). Evaluate: ] f(x)dr

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Q: (d) tan¹(x)dr

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Q: Determine the order of the zero at the origin of f(x) = ² (cos(z) - 1 + sin² (2))

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Q: Apply the special case of the general power rule d/dx [h(x)]2 = 2h(x)h(x) and the identity fg =…

A: dhx2dx=2hx·h'x  &amp;  fg=14f+g2-f-g2

Q: ) Define the domain and range of f(x) where f(x) = sin²(x) – 1

A: The function f(x)=sin^2(x)−1 is defined for all real numbers x because the sine function, sin(x), is…

Q: Sketch the graph of the function f(x) = 12 x sin x on the interval [−3π, 3π]

A: we have to sketch the graph of the given function at the given interval. f(x)=12xsinx on the…

Q: Use logarithmic differentiation to find dr y = (x'+x}/x³ +6 Oa. ( 3x²+1 3x² 2x³ + 12 ´ 3x² + 1…

A: first use logarithmic property and then differentiate it.

Q: State the set of zeros of f(x)=2sin(x)cos(x) using set builder notation.

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Q: (2) Let f(x) = -3 sin (r +). (c) And then determine the domain and range of f(x).

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Q: 150. dx), V9 – y²dy 3

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Q: Use trigonometric substitution to evaluate the integral (a) arcsin(r)+C 9x 9 - x² √9-x² (b) 9x + C…

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Q: 18. Fill in each blank with an interval of real numbers. (a) The function f(x) = cosx has domain and…

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Q: Prove the identity arcsinhx=ln(x+√1+x2).

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Q: B. Prove the following: NO Differentiation 16-x 4. lim 1x16√x-4 = -8 sin 5x 1 x→0 sin 10x 2 5. lim…

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Q: Consider the functions: f(x) = (cos(x) − sin(x))/cos(2x) and g(x) = 1/(cos(x) + sin(x)) where in…

A: cos(2x) = cos^2(x) - sin^2(x)

Q: Prove that: 3 (0) 2³ ( 1 - 4 ² ³ ; x ²) = + sin²¹ x (b) 2₁ (¹-x²) == tan²¹ x 1 H

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Q: 1 + X tanh (x) 1 In 2 - 1 - X

A: The solution is given as

Q: list the three transformations being applied to f(x)= 4 sin(4(x-5))+5 parent function: f(x)=sinx

A: To find- List the three transformations being applied to fx = 4sin4x - 5 + 5.  Parent function: fx =…

Q: 1 f (x) = x4 – Vx³ + x$

A: The function is given by fx = x4-x3+x18 To evaluate: The derivative of the function.

Q: Calculate the derivative d dx t14 + 5dt using Part 2 of the Fundamental Theorem of Calculus.

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