The graph of y=f(x) is given. Solve the inequalities. Write the solution sets in interval notation if possible. y = √(x)

Q: | 6. Use a trigonometric substitution to evaluate x³√x²-4 dx.

A: We will find integral using  trigonometric substitution.

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A: Taylor series ;             In the more compact sigma notation, this can be written as…

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Q: 1- Consider the following nonlinear 10x - 3+e-³-2³ sin(x) = 0. a) Prove that the nonlinear equation…

A: GIVEN:- 10x-3+e^(-3x)-x^3sin(x)=0

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Q: The derivative of y = -ln(cos(ex + 1)) is

A: Our Aim is to find the derivative of y=- ln cos ex+1 -(i)

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Q: if f(4)=2 and f'(4)=2/5, use the formula (f-1)'(x)=1/(f'(f-1(x))) to find (f-1)'(2)

A: If f is an invertible function and if f(a)=b, then f-1(b)=a.

Q: 7. Two part question: a. Determine the equation for the slope of the secant line between the point…

A: The given problem is solved below in detail.

Q: The trigonometric integral fs sec² x (tan³ x - 2 tan7 x) dx is equal to

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Q: 5. Evaluate 8y L L (PS4 12 dzdy + 1)² by reversing the order of integration.

A: Follow the procedure given below.

Q: The trigonometric integral [sec² x (tan³x - 2 tan² x) dx is equal to

A: SOLUTION-

Q: uestion 3 Find f(x+h)-f(x) given the following function. Answer f(x+h)-f(x) = | کے f(x) = 8x² + 5x

A: The solution is given below

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Q: x'+z=et; x(0) = 1

A: Take z as constant

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Q: Take xlt) then x (1) = => x/w) = -jut J'est dt 1.e => x(w) == 1 JW X(w) = Lx -jwt ax e [f10+ ] ~ Sex…

A: To check the +ve or -ve

Q: By double integration, Find the area between the line y=6-2x, the x-axis and y-axis.

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Q: 1.Add the following displacements by the component method. 8.0 ft directed 45º northeast, 12.0ft…

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Q: Letter E

A: Solving letter (E)

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A: This is a basic limit problem

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Q: sin x +∞0 Σ n=0 (-1)" (2n + 1)! px?nts] for all x € R

A: Ans: 0.099999983 Solution is attached below.

Q: Using an appropriate substitution, the integral [x² x² csc²(x³) cot(x³) is equal to - dx - In…

A: Given ∫x2 csc2(x3)cot(x3)dx Formula: ddx(cot x)=-csc2xddx(xn)=nxn-1 Consider ∫x2 csc2(x3)cot(x3)dx…

Q: 2x²+5 1. Answer the questions below and then graph the rational function: f(x) = x²+x-2 a. Vertical…

A: To find out the vertical asymptote, vertical asymptotes and also make the graph.

Q: Write the first five terms of the recursively defined sequence. 12 ak 2² a₁ = 4₁ ak + 1 Step 1 Note…

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Q: A company wants to start a new clothing line. The cost to se up production is 35, 000 dollars and…

A: The solution is given below

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Q: Given the integral expressions for F and G below, select all statements that are true. F = [₁² (5x²…

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Q: Find the derivative of y = (10x) x² + ₂

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Q: Differentiate implicitly to find the first partial derivatives of z. 5x² + 11y² + 7z² = 4 (No…

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Q: The cost of producing 420 calculators is $2320. Producing 580 calculators would cost $3120. Step 1…

A: The cost of producing 420 calculators is $2320. Producing 580 calculators would cost $3120. To find…

Q: 12. Determine the radius and interval of convergence of 8 k=1 (-1)kk²(x-4) k 3k

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Q: P7:TE %7 02 7 The derivative with respect to x of the function y=-3tan-¹x-(In 3) log; (csc x) is y'…

A: Given: y=3tan-1x-ln 3log3csc x

Q: Take xlt) then x (10) = X => x/w) = Ś j'₁. é just dt = x(w) == 1 ζω X/W) = Lx -jwt -jw jw -jw 1 -…

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Q: Consider the relation R defined on the set X={a,b,c,d} and Y={1,2,3,4} from X to Y, where R= {(?,…

A: Disclaimer: Since you have  asked multiple question ,we will solve first question for you . if you…

Q: 11 7 Find Y 12 2r₁²³² + y² = 4 2

A: here is the solution

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A: We know that the directional derivative of a function f(x, y) at a point P in the direction of a…

Q: 4. Given f(x) = sin² (2x) find the slope at (5, 1) a)-√3 b) √3 d) 0.1395

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…