Consider the function. f(x) = -2x3 + 12x² – 24x + 15 Step 2 of 2: Determine the open intervals on which the function is increasing and on which the function is decreasing. Enter Ø to indicate the interval is empty.

Q: 1) Find parametric equations for the line which contains A(2,0, 1) and B(-1,1, –1).

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Q: Every function defined on a closed interval [a, b] must have a global maximum and a global minimum o...

A: Find your answer below 

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an imprope...

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Q: tan A - sec A = sin A-1 cos A 2 sin A- cos A cos A O cos A-1 cos A

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Q: Find the values of x for which the series converges. (Enter your answer using interval notation.) (x...

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Q: sin-"(ry) = cos-'(x – y)

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Q: 13 Given: cosa = and a is located in the fourth quadrant; find tan 29. -14/27 24/7 -24/27

A: I am going to solve the given problem by using some simple calculus to get the required result of th...

Q: Select the best answer. cot A sin 2A =

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Q: Consider the following. dt 49 + t2 Let t = 7 tan(0) and determine the following. %3D dt d0 t = 0 → 0...

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Q: Given: sin a= and sin B= , 0< a < and 0 < B< ! Find cos(a + B) 33/65 14/65 63/65

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Q: -7 dx Vx-9 3

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Q: A rocket is fired vertically upward from the ground. The distance s in feet that the rocket travels ...

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Q: Every function defined on a closed interval [a, b] must have a global maximum and a global minimum o...

A: Every function defined on a closed interval a,b must have a global maximum and a global minimum on a...

Q: Slopes and Tangent Lines In Exercises 13–16, differentiate the functions and find the slope of the t...

A: Given,

Q: For the equation given below, evaluate y′ at the point (1,1). y-3x^2+2=0 y' at (1,1)=

A: Given equation differentiate w.r.t.x

Q: Given: cosa= -1, sin x = - 12, A is in the third quadrant, and x is in the fourth quadrant; evaluate...

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Q: Second Derivatives In Exercises 19–26, use implicit differentiation to find dy/dx and then dy/dx². W...

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Q: Obtain the solution using Integrating Factors Found by Inspection y(x3y3 + 2x2 − y)dx + x3 (xy3 − 2...

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Q: Find the equation of the line tangent to the given curve at x = a. Use a graphing utility to graph t...

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Q: Let f(x) = x- 2x- 9. a. Find the values of x for which the slope of the curve y = f(x) is 0. b. Find...

A: Topic:- derivatives

Q: (a) If U(x, y, z) = xy'z', find VU and VU. (b) If V(p, d, z) = sin d find VV and VV. (c) If W(r, 0, ...

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Q: he position of the particle at timet is given by s(t) =ť² – 4t + 3. The particle is moving from righ...

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Q: 2. Use parametric equations to derive the formula for the lateral surface area of a right circular c...

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Q: = - 13, e is in the third quadrant, and x is in the fourth quadrant; evaluate tan 29 24/5 24/7 12/13

A: Here we will find tan2θ,

Q: A Geometric Series is the sum of an infinite terms that the ration of two consecutive terms is a con...

A: We need to prove the following geometric series by induction:1+r+r2+r3+...+rn=rn+1-1r-1

Q: cot2 x – cos2 x = ________ cos 2 x sin 2 x sin 2 x cot 2 x sin 2 x tan 2 x cos 2 x cot 2 x

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Q: Find the derivative of the function and evaluate the derivative at the given value of a. X = (x)4 ;a...

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Q: a Identify the inproper intergrals an ex plain (briefly) why it is improper () e 5 dX D x-ス ーメー2

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Q: In Exercises 17–18, differentiate the functions. Then find an equation of the tangent line at the in...

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Q: If x = c is in the domain of f such that f'(c) = 0 and f"(c) > 0, then f has a local maximum at x= c...

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Q: Find the derivative using the formula f'(x)= g'h + gh' 1. cos x cot x

A: Differentiation

Q: sc 2x - cot 2x = 0 1 sec

A: We have csc2x-cot2x=?

Q: 3x2 + 5x + 11 Evaluate / dr. (x+ 1)(x² + 2x + 10)

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Q: Solution of ODE: Find the solution for the following ODE y' = 2y O y = ce2r O y = 2ce"

A: Topic - differential equation 

Q: Given h(x, y, z) = 4Vx+ ln (y² + z²+1). (a) Find the directional derivative of h at the point (1,0, ...

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Q: 3. a) Use the trapezium rule with five ordinates to find an approximate value for S dx, giving your ...

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Q: Given a function g(x, y) defined implicitly by the equation z*y* + sin (x² – y²) = tan-'(xz). (1) dz...

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Q: 8x2 + 8x + 2 dx (4x² + 1)

A: 4x^2+1 cannot be fractionised further

Q: The table shows values of a force function f(æ) where a is measured in meters and f(x) in newtons. U...

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Q: 1 J 2x2-3x+2 dx;

A: solution:-∫12x2-3x+2 dx=∫24x2-6x+4 dx=∫22x2-2·32·2x+94+74dx=∫22x-322+74dx

Q: Elimination of arbitrary constants.

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Q: If x = c is in the domain of f such that f'(c) = 0 and f"(c) > 0, then f has a local maximum at x= c...

A: The given problem is solved below in detail.

Q: 2x+6)dx x²+2x+5

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Q: Find the derivatives of the functions in Exercises 17–40. 2 – 1 2 + t – 2 20. f(t)

A: Given:- f(t) =(t2 -1)/(t2+t-2) To find:- Derivative of given function f(t) 

Q: A rocket is fired vertically upward from the ground. The distance 8 in feet that the rocket travels ...

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Q: 3 If z= then: (2x² + y² )² ' dz az + y- -4z he dz dz + y- 4% az dz + x- y- = 4z az az = -4z

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Q: Evaluate the integral. 3. Vx² + 9 dx V x2

A: Evaluate the integral  of √(x2+9) from 0 to 3. 

Q: Determine whether the series converges. 1 A V5k – 1 k=1 O The series converges. O The series diverge...

A: 1 ∑k=1+∞15k-13let f(x)=15x-13By integral test∫1∞15x-13=lima→+∞∫1a15x-13dx=lima→+∞∫1a(5x-1)-13dx=lima...

Q: 2. STO Find the length of the graph of y = 2+ In(sin z) om the interval [7/4, 7 /2].

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Q: Find all values of x at which the tangent line to the curve 2x + 11 is perpendicular to the line y =...

A: Given curve, y=2x+11x+5 Aim: To find the value of x at which tangent is perpendicular to the line y=...