Prove the following: sin² 0 – cos² 0 = 1– 2cos² 0 %3D

Q: a) lim x-3 x+1 x2 – 4x + 4 b) lim x-2 x2 +x - 6 y? – 4y – 21 c) lim y-7 3y2 – 17y – 28 t3 +t2 – 5t +...

A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant an...

Q: conditions for each equation: d²x 2 dx (a) + x = 1 dt F(0) = F'(0) = 0 %3D %3D dt2

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Q: (Зп + 1)! Find the limit of the sequence an = If the (Зп — 1)! limit does not exist, type "Diverges"...

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Q: An inverted pyramid is being filled with water at a constant rate of 45 cubic centimeters per second...

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Q: For a given function f, what does f' represent? Choose the correct answer below. O A. f is the avera...

A: Solution: Given data, f is a function f' represents??  

Q: of the initial value problem gcナー Please fill in a question quickly within a quarter of

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Q: Consider the surface. z2 = 25y %3D Identify the surface. O cylindrical surface O paraboloid O hyperb...

A: We have to identify the surface z2=25y.

Q: Find the solution of the initial value problem Please fill in a question quickly within a quarter of...

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Q: Find an equation of the tangent(s) to the curve with parametric equations E = t cos t, y =t sin t nt...

A: follow next step

Q: Write the equation of a parabola whose directrix is y = - 0.75 and has a focus at (– 8, 8.75).

A: Let's find. 

Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

A: Find your answer below 

Q: Recycling Programs The commissioner of a particular city's recycling program assesses that the amoun...

A: for 2008 here t = 8 so put t = 8 in equation N(t) = (200,000)/(2.5 + 3e-0.5t) N(8) = (200,000)/(2.5 ...

Q: 5. Find the point on the parabola y=2x-3x+6 where the tangent line is parallel to the line 7x+y=1.

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Q: Write a differential equation that models the given situation. The stated rate of change is with res...

A: The objective is to write the required differential equation.

Q: Problems: Find the general solution y9-2y9+y"=0|

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Q: .Evalnate. the following.denble.integral.s.by.conver.ting. bo ... polar.Coa.r.dinates. .... Ans: 36 ...

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Q: Recall y" Second Derivafive Analy'sis goals O track intervals of positive $ = -6x(x²_ax+4) (xta)? (x...

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Q: Find the are length of the curve y² = 3x between the from x=0 to x=9 ! Use integral approximation! %...

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Q: TE: Enter the exact answers in terms of i,j and k. Same direction as – 3i + 5j. u = Oppositely direc...

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Q: Sketch the region bounded by the given curves, then find its area. 1. y = x², y = 2x

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Q: solve for 0 ≤ Θ < 2pi    ,                                            Θ = theta -cosΘ+sinΘ=1

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Q: f(a + h)-f(a) a. Use the definition man = lim to find the slope of the line tangent to the graph of ...

A: The given definition of the slope of the tangent line of a graph at the point P is: mtan=limh→0f(a+h...

Q: 9. Use the following graph to find the coordinates of the point where the lines y =-2x+6 and y = 3x+...

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you wa...

Q: Given the funcfion y = -x3 (x ta>(x-1)

A: Question- First Derivative Analysis 1. track intervals of increasing &amp; decreasing,so include a f...

Q: Consider the points A(3, –3, 3), B(4, –5,0), C(-3, -4,0), and D(6, 2, –6). | (a) Find the volume of ...

A: AB→ =B-A      =(4, -5, 0)-(3, -3, 3)AB→ =(1, -2, -3)AC→ =C-A      =(-3, -4, 0)-(3, -3, 3)AC→ =(-6, -...

Q: Sketch the region R whose area is given by the iterated integral. *16 – y² dx dy 14 12 10- y 8. 4 2-...

A: Solve by using graph

Q: (b) Oppositely directed to 6i – 4j + 2k. 6 i v = V56 2 k + V56 V56 (c) Same direction as the vector ...

A: Given problem:- Find unit vectors that satisfy the stated conditions. (b) Oppositely directed to 6i-...

Q: Find an equation of the tangent(s) to the curve with paramnetric equations ¤ = 1+ VE, y = e" at the ...

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Q: Find the limit. Use l'Hospital's Rule where appropriate ex + e-X - 2 lim x-0 ex – x – 1

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Q: Find the area of the region enclosed by the graphs of 1 1 =0, and x = 4 y = 0, x V1– 4x? - NOTE: Ent...

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Q: Determine where the function is concave upward. ​   ​f(x)x^4-2x^3+7x+5

A: Given: - The function is, f(x)=x4-2x3+7x+5 To determine: - The concave upward of the given function.

Q: 6. Graph the linear inequality on the graph. m. y2x-5 %3D %3D

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Q: Let f(x, y) = xy – y + cos x. af Find (a) fe dy and (c) the mixed partial fæy. (b) O (a) xy - y (b) ...

A: Find your answer below 

Q: Find a polynomial equation that passes through the points (1,3), (0,1), (1,3)

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Q: Match the quadric surfaces to its graph. A. y? + 22 = 4 + 4x? C. 9x? + 4y? = 36 + 36z2 B. 4x2 + y? +...

A: This is a problem related to the curve plotting in the 3 dimensions. Based on the available concepts...

Q: Find the area of the triangle with vertices P(1, 2, –5), Q(0,0,0) and R(4, 6, 1). NOTE: Enter the ex...

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Q: Approximate the sum of the series correct to within 0.00001. (-1)" (3n)! n = 1

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Q: What is the point of intersection of the following line and plane: line: 7 = [3, 1, 2] + t [1, - 4, ...

A: Given  r⇀=3,1,2+t1,-4,-8&amp; plane π=4x+2y-z-8=0 To find point of intersection:

Q: 1. Approximate the area under the curve of y = e¯** from x = 0 to x = 1 using: a. R4 h Le %3D

A: Reimann sum

Q: Consider the parallelepiped with adjacent edges u = 5i + 9j + k v = i+j+ 3k w = i+ 5j + 7k Find the ...

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Q: 8) Find 4 given : f(x)=- (3x² – 2x +1)'

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Q: y = cos(2x), y = sin x, 0<x< 2

A: Solution is given below:

Q: Use Taylor's Inequality to determine the minimum number of nonzero terms of the Maclaurin series for...

A: Use the Taylor's inequality to determine the minimum number of nonzero terms.

Q: Two entrances E and F to a gym are located 1 m away from a wall AB of length 4 m which is perpendicu...

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Q: Sketch the region bounded by the given curves, then find its area. 1. у%3D х*, у%3D2х

A: Since the student has posted multiple questions and does not mention any specific question, so we ar...

Q: e)S 2х-4 dx х3+5х

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Q: ハメー X1 YxJ dx |

A: Find the integral

Q: function f(x) = x² ose x-coordinates are -2 , 0, and 1. 2x and draw the tangent lines to the gr 10 4...

A: We will draw the graph and the tangents. 

Q: uation of the plane that contains the lin y = 5+3t, z =-1-4t

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Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at 6...

A: Question- If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continu...