9. From "First Principles" show that if f(x)= == 2 x²-3' then f'(x) = - 2x (x² - 3)²

Q: Consider the two equations y = 2x + 1 and y = x² - 4x + 9. A. Without computing any sample xy-pairs…

A: Given 1. y=2x+1 2. y=x2-4x+9

Q: (x + y − 1)dx + (2x + 2y + 1)dy = 0 www.

A: Replace y+x by u

Q: Use graph in the photo to determine: a. open intervals on which the function is increasing if any.…

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Q: 13. Which graph matches the polar equation below? 9 r = O ·? 3- cos 0 A. + B. + 3 5- 4- 92…

A: Solution:

Q: Suppose that a point P has, respectively, spherical coordinates, rectangular coordinates, and…

A: The coordinates of point P is given as , Rectangular coordinates = x,y,z Spherical coordinates =…

Q: 7 L+₂hε =₂ h ₁₂x-hubt E C ६

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Q: R is the region bounded by the functions f(x) = 1 - 3 sin (x) and g(x): the functions on the…

A: The function is given by fx = 1-3sinxgx = 2cosx To evaluate: Area of the region bounded by the…

Q: a) What is the half-life of the element? alf-life: (days) b) How long will it take for a sample of…

A: Topic:- calculus

Q: If a = (5, 0, -1), find a vector b such that comp₂b = 2. b= ||

A: I have appended the formula used in the solution part of the question

Q: Find the inverse transform of the given function of s. F(s) = A C -4s² - 6 (s + 4Xs +6Xs - 7) D f(t)…

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Q: Find f'(x). 4 f(x) = 3x5 (x² - 4) X

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Q: Determine whether the given vectors are orthogonal, parallel, or neither. (a) a = (9, 6), b = (-4,…

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Q: Express the plane z = x in cylindrical and spherical coordinates.

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Q: Find all values x = a where the function is discontinuous. For each value of x, give the limit of…

A: The given function is: Px=|x+2|x+2

Q: ind the equations of the tangents to y = 2x³-16 at the points where the curve touche the x-axis.

A: Topic:- application of derivatives

Q: Solve for the inverse Laplace transform. of the function in f(t) form: R(S) 5s (e²+1) 5 e 4 64 5²…

A: see below the answer and calculation

Q: can you check if my procedure and answer is right?

A: I am answering this question.

Q: Finding a Particular Solution In Exercises 37-42, verify that the general solution satisfies the…

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Q: 1. Straight lines with with slope and x-intercept equal

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: If f(x) = 3x² - 7x + 6, find f'(-4). Use this to find the equation of the tangent line to the…

A: Given function:- fx=3x2-7x+6

Q: DIFFERENTIAL EQUATION (6²-2xy²) dy 1. (2y³ +4²) dx = 1 2. 2yy" + (y)² = 0 3. (2xy) dx + (y² + x²)dy…

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If it…

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Q: Using the binomial theorem formula expand the following: b) (2 - 3x)²

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Q: g(a,b) = a²b-2a² - 4a + 2ab. Determine all the critical points of g. And determine the relative…

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Q: Consider u = [-3, 6] -3, 6] and = [4, 2]. a) Without determining the angle between the vectors,…

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Q: Consider the triangle with vertices P(0, -4, -1), Q(1, -1, -3), and R(5, -3, -4). Determine the…

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Q: Find the derivative. (5x6+8x3)4

A: The function is given by y = 5x6+8x34 To evaluate: The derivative of the function.

Q: The graph to the right shows a region of feasible solutions. Use this region to find maximum and…

A: see below the answer and explanation

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

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Q: 5. If y=5x²-3x + 10, give y'(-1)

A: We have to find the y'(-1).

Q: (a) 2xy + y² 2xy³ + 2x²y²x² - 2xy da (b) x(y + x)²y = y³ + 2xy² + x²y + x³ da

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Q: In Exercises 117-119, perform the indicated operations. 1 1 1 117. x" - 1 x" + 1 2n 1 (1 -) - 1 1…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A simplified polynomial that has two terms is called a/an .-----------------------------

A: A polynomial may have one term, two terms or many terms.A polynomial with single term is called as…

Q: 13. Graph the solution set of the system of inequalities: y 8x - 3 O O A. <++++++ -20 10 B. <++++++…

A: Topic- System of inequalities We are given ,y&lt;-x+8 y&gt;8x-3 in slope intercept form , y=mx+c…

Q: 36. The 28th term in the expansion of (A - B)30

A: Formula: nth term in (x+y)n expansion is Tr = nCr-1 xn-(r-1).yr-1

Q: Find the area of the region that is bounded above by the curve f(x) = (x + 2)² and the line g(x) =…

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Q: Evaluate the expression under the given conditions. 5 13 cos(p); cos(0) 5+5√ 15 26 = 0 in Quadrant…

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Q: Find the inverse transform of the given function of s. F(s) - 5/4 A B C D E f(t)= t3 O (t) = -54³…

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Q: To multiply 7x*(4xs – &r? + 6), use the property to multiply each term of the by the monomial…

A: Given product of polynomials is Px=7x34x5-8x2+6

Q: Solve for the particular solution of y' = 1/1 e 42 +3 sin 2x when x = 0 and y = 1

A: The differential equation is given by y' = 12e4x+3sin2x The initial condition is  y0 = 1 To…

Q: Find the inverse transform of the given function of s. F(s) A f(t)=354-736- 11 B -45²-6 s+4Xs+6XS-7)…

A: A detailed solution is given below.

Q: Can I square the right side of V2r - 1 = r – 2 by first squaring x and then squaring 2?

A: Given data:- 2x-1=x-2

Q: The center of a circle is (h,7) and the radius is 10. The circle passes through (3,1). What are the…

A: Please see the below picture for detailed solution.

Q: Question 1 Using the binomial theorem formula expand the following: a) (2x + y)²

A: We know that binomial theorem (a+b)n=nc0anb0+nc1an-1b1+nc2an-2b2+. . ..ncna0bn

Q: Let f(x) = 3x - 5x² - 3. Find the equation of the line tangent to the graph of y = f(x) at the (2,…

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Q: Let f be a function such that Evaluate the limit lim ef(x) - 1 x3 2x6 ef(x) - 1 x3 2x - 6 (a) lim…

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Q: 2. An ellipure is defined by parametric equations follows as X= 5 sin (b) y = 7 cas (6)

A: According to bartleby guidelines for multiple question I can answer only one question. You can…

Q: 2) 1 – xу = x — у -

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Q: Find y' by (a) applying the Product Rule and (b) multiplying the factors to produce a sum of simpler…

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Q: Find the following limits (a) by investigating values of the function near the x-value where the…

A: Consider the limit  limx→2x4+x−18x2−4