2. Find the equation of the tangent line to the curve y = x³+ 2x² – x at the point (-2, 7).

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Q: u=(+4,-9) and V=(3,-2) 0 Find the dot product of = %3D

A: Given: Vectors: u=(-4,-9)v=(3,-2)

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A: Topic:-  application of integration

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A: Topic:- limit Calculus 

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Q: Use the product rule to find the derivative. f(x) = -2xex? %3D Please show all steps

A: To find the derivative of given function.

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A: Use simple continuity theorem.

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Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line. 36x2 +...

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Q: Question 5 Find the value or values of c that satisfy the conclusion of the mean value theorem in th...

A: Use mean value theorem

Q: Determine if the given function y = f(x) is a solution of the accompanying differential equation. y'...

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Q: 1. Find the general solution of the differential equation: dy, dy + dx3 dºy dy = 0 dx6 dr5 dx?

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Q: A. Determine whether the graphs of the following are continuous or not. Write yes if it is. Otherwis...

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given ...

A: The equation of the plane P which is normal to the vector n and passes through the point R is given ...

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Q: A hall 110 feet in length is to be designed as a whispering gallery. If the foci are located 20 feet...

A: Find your answer below 

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A: Find your answer below 

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Q: . 2а3 + 5а? — 7х + 16 at a — 3

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

Q: Let f (x) = 3x, g (x) = x + 1. Find the composite function. ​

A: f(x)=3x  ,   g(x)=x+1Two composite functions can be defined(f∘g)(x)  and ( g∘f)(x) Consider(f∘g)(x)=...

Q: Question 10 Finding the Domain and Range of a Function: f (x) = Vr² – 3x + 2. 0(-0, -2 JU [1, 00) O(...

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Q: d²y -6空+9= 0. dx2 dx 业

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Q: You have been which of them are given the following continuous at functions 10,0)? More than one rig...

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Q: Determine the point(s) where the tangent to the curve is horizontal: y = (x2 + 2x + 1)(x2 + 2x + 1)

A: Given problem:- Determine the point(s) where the tangent to the curve is horizontal:   y = (x2 + 2x ...

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Q: Use a change of variables or the table to evaluate the following indefinite integral. dx e ex +5 Cli...

A: We have to find the integral

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Q: A piece of wire 28 m long is cut into two pieces. One piece is bent into a square and the other is b...

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Q: 1. Consider the function f(x) = {x + 2, values to find the limit of the following: - x - 6, x > 0 x ...

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Q: Find the derivative of the trigonometric function. y = 4 sin(3nx)

A: The given function is: y=4sin3πx   We know that; The Power law: ddxxn=nxn-1 The chain rule: fgx'=f'g...

Q: Which of the following functions is continuous at x = 0? S x+1 if x 0 b. sin(x) if x 0 Ос O c. Non...

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Q: The points (6, 9, 7), (9, 2 , 0) and (12, -5, -6) lie on the same line. True False

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Q: Find the zeroes of the functions algebraically. x2- 14x+ 48 f(x)= 7x x = 8, x = 6, x= x= x =-8, x = ...

A: Explanation of the answer is as follows

Q: Find the area of the shaded region. The image is not to scale. x= -cy Ay x=d- y? Consider c=1, d=2. ...

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Q: dx dy =1.95. dt Given y = x. Find when y= 3 and %3D - - dt (Simplify your answer.) dt

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Q: Calculate M6 for f(x) = v6x over [3, 6]. (Use decimal notation. Give your answer to two decimal plac...

A: The function isf(x)=6x over [3,6].The number of sub-intervals is n=6.

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Q: Find an equation of the tangent line to the curve 2(2² + y?)? = 25(x² – y²) (a lemniscate) at the po...

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Q: Let f : R2 → R be defined by f((x, y)) = x² + 2y – 3xy, for every(x, y) E R² - The value of fx((0, 0...

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Q: Find the derivative of the function j(x), below. Assume that c and d are constants. j(x) = In(e" + d...

A: answer of given question is in step 2

Q: Evaluate the integral. (Hint: rewrite cot, do u-sub) 7π/3 4 cot dt 7n/6 O 28 In 3 -14 In 3 -28 In 3 ...

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Q: Let f(x) = 6 sin- (x³) f' (x):

A: Basic identities of differentiation are used