Find the critical numbers of the function. f(x) = x³ + x?

Q: Find the derivative of g(x)= using the limit definition

A: Solution:we have use formula g'x=limh→0gx+h-gxhgx=1x-1g'x=limh→0gx+h-gxhg'x=limh→01x+h-1-1x-1h=limh→...

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

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Q: The graph of f (x) is provided below, select the approximate value for the derivative at each point....

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

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Q: Consider the following equations. F(x) = Vx + 5 g(x) = x + 5 %3D Sketch the region bounded by the gr...

A: Graph of the curves÷

Q: Find two unit vectors in 2-space that make an angle of 45° with 5i+ 4j. NOTE: Enter the exact answer...

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Q: Evaluate the following integral. | e2* cos3x dx

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Q: Find the area of the parallelogram that has u = i – 2j +k and v = 3j + 2k as adjacent sides. NOTE: E...

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v and w is...

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Q: Ax) = ,5-9,4+73 -5,2 -8x+1 is continuous on (-o, co) because fx) is a polynomia and polynomials are ...

A: The objective is to state true or false of the above question.

Q: Set up an integral for the area of the shaded region. Evaluate the integral to find the area of the ...

A: f1(y)=4y-y2f2(y)=y2-6yArea bounded;0≤y≤5A=∫05f1(y)-f2(y) dyA=∫054y-y2-(y2-6y)dyA=∫0510y-2y2 dyA=2 ∫0...

Q: 28. 5 29. (x + 1)(x – 1) 30. 을 (x-1)5

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Q: How can we determine this unit circle by filling them?

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Q: A math tutor charges $30 for the first hour of work at your house and $20 for every hour (or fractio...

A: Use the value of x for finding the limit. 

Q: Using the function f (x) = 2x2 - 3x 1, find the average rate of change of f (x) in the interval 1,3]...

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Q: 2xy +y+1 x+2xy dy dx

A: Topic:- differential equations

Q: (1) As x→ t0, the end behavior of the polynomial p(x) = 3x°(1 – 2x + x°) can be resembled as (A) p(x...

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Q: Write an equation for the polynomial graphed below 4+ 2+ 2. -1 -3. -4- -5- y(x) = 2.

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Q: Coal gas is produced at a gasworks. Pollutants in the gas are removed by scrubbers, which become les...

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Q: 2- Prove that: Jzt=27 dz %3D 2in. Whot is the princinle nart for f(z) = ze %3D

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: 3. The diagram on the right shows an open box with a square base of side x cm and a height of h cm. ...

A: a)Area of the box (A)=x.x+2xh+2xhA=x2+4xh75=x2+4xh  [Since A=75 cm2]75-x2=4xhh=14x75-x2Volume of the...

Q: The first derivative of a continuous function y = f(x) is given. Find y" and then sketch the general...

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Q: rtoo Е. re dx स०२२

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Q: The sides of a square increase in length at a rate of 3 m/sec. a. At what rate is the area of the sq...

A: lets the size of square is l so the rate of change of length = dl/dt = 3 m/sec area of square = l2 r...

Q: Consider the points A(1, -1, 2), B(2, –3,0), C(-1,-2,0), and D(2,1, –1). (a) Find the volume of the ...

A: Here, the given vectors are: A(1,-1,2), B(2,-3,0), C(-1,-2,0) & D(2,1,-1) (a) Here, AB=(2,-3,0)-...

Q: 2. Find the derivatives of the following equations: y = sin-'(1 – t) y = csc-'(x/2) CSC y = In(tan¬1...

A: Note: - Since you have posted a question with multiple sub-parts, we will solve the first three sub-...

Q: Find the volume V obtained by rotating the region bounded by the curves about the given axis T y = s...

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Q: Which is the better base for working with exponents and logs : e or 10? Justify your answer.

A: log with base e is better for working with exponents.

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

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Q: B - Find the equation of the curve whose slope at any point p(x.y) is m = x(x+5)² , and passing thro...

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Q: Find two unit vectors in 2-space that make an angle of 45° with 6i + 5j. NOTE: Enter the ezact answe...

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Q: Find the radius and interval of convergence of the given power series. +o0 (x +3)" Σ 1. n5 +1 n=0 +0...

A: Given problem:-     To find:- Interval and radius of convergence of given series

Q: Which of the following is the derivative of f (x) = 6/a O r(2) f' (x) = %3D 3 f' (æ) = %3D O f' (x) ...

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Q: lim, 00 f(x) = lim, 4 f(x) lim, -1 f(x) = f (4) =

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Q: Evaluate the given integral, choose the answer in the box 1/(t-1) 2x S(-1)^5(x-1) -2/(x-1)^2 2/(t-1)...

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Q: 1. (a). Find the linear approximation to f(x) = VT at a 81, (b). use it to approximate 85. (c). Comp...

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Q: Evaluate the given integrals. 2. S sin?x sin 2x dx

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Q: Find the area of the region bounded by the curves, x = -6, x = 6, the x – axis and the parabola x2 –...

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Q: Question 3 Find the center and radius of the circle whose equation ís z² + 4z + y² – 1 = 0. The cent...

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Q: for power substitution method, next step is * For Sdz 16 – 5(u²)â + u² -(2udu) 4 – u? r6 – 5u² + u? ...

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Q: Identify the local extrema of f(x) = x³ – 4x² + 4x O Local Maximum of 2 at x=0 and Local Minimum of ...

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

A: v=19, -12oppositely directed to v,(The angle between vectors with opposite direction is 180° and the...

Q: Let 1 f(z) = I - 3 Use the limit definition of the derivative to find (i) f'(– 1) = (ii) f'(2) = (ii...

A: Solution is written in below steps.

Q: Use the fact that the volume of a tetrahedron with adjacent edges given Edit 1 by the vectors u, v a...

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Q: Jo 17. cos² x sin? x dx

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Q: 1) ? 65° 57°

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Q: Find the area of the parallelogram that has u = i – 2j + k and = 3j + 2k as adjacent sides. NOTE: En...

A: Area of parallelogram with adjacent sides u→ and v→ is defined as u→×v→

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = t2i 1,3K 4tj + %3D (a) r'(t) (b) r"(t) (...

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Q: 1 1. lim In (x- 2) x-3 X-3+

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Q: Robinson makes $200 a week and spends his entire income on running shoes and basketball shorts. Writ...

A: We have to find the algebraic expression for the above statements.