Find the area of the region bounded by y = -x² – 4x – 2 and y = 2x2 + 8x + 7.

Q: Let a = ci +j and b = 4i + 32j. Find c so that a and b are orthogonal. C = i

A: Recall: If two vectors a and b are orthogonal then their dot product is zero that is a·b=0

Q: DO NOT include spaces in between characters. Type your answers in the following order and format: a=...

A: Given query is to find the value of a and b.

Q: a2 - 3x + 1, r 3 Evaluate the following limits for h(x) = and Justify your answer. (i) lim h(x) I +...

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Q: Question 3 Determine whether the improper integral converges or diverges. 14e5x dx A Diverges B Conv...

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Q: why should y>0 ?

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Q: 6 The coefficient of sin( 2x) in the antiderivative of F(x) = cos is Blank 1 (use fraction form not ...

A: ∫cos6(x2)dxsubstitute u=x2→dudx=12→dx=2du=2∫cos6u du=2[cos5u.sinu6+56∫cos4u du]=2[cos5u.sinu6+56[cos...

Q: 00 e-2y dy 0.

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (– 1)k+1 4k k=...

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Q: 4 Find the value of f'(-1) if ƒ (x) = (3r² – 2x +1)'

A: Given,            fx=43x2-2x+13To find : f'-1

Q: Sketch a graph of the function y = 3x2 – 8x + 5. Use calculus to find: %3D a. increasing and decreas...

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Q: Find the domain and range of -4 < a<0, f(r) = 0 <r<4.

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Q: Find a function y(x) such that 5yy' = x and y(5) = 8. y =

A: Given: - The differential equation is, 5yy'=x and y(5)=8 To find: - The function y(x) such that the ...

Q: 2 cos 20 sin? 0 + 2 cos 0 cos 20 sin 0 + cos 20 cos? 0 d0 (use trigonometric integrals)

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Q: An inverted pyramid is being filled with water at a constant rate of 75 cubic centimeters per second...

A: The rate at which water level is rising when the level is 5cm is 25cm/sec.

Q: dy There is no need to simplify. dx 2. Find cos- (sin x) – sech(tan-x) a. y = ecosh a

A: Find your answer below 

Q: aracters. * mine the slope of the tangent line to the graph of f(x)=-- at the point (4,-4).

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Q: 3. +4 Use the ehain rule to find devinitine

A: Here we have, y=x2-22x3+44 Differentiate with respect to x,   

Q: Determine f'(1) if f (t) = log10,ti t+1 17 Your anSwer

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Q: xsin-xdx The antiderivative of V1-x? sin-!x+C is x- (A True (B) False

A: The given integral,∫x sin-1x dx1-x2

Q: Find the points on the graph of f(x) = where the tangent line is horizontal. x2+2

A: Given query is to find the points where tangent is horizontal.

Q: Determine the area of the trapezoid 8 ft 15.6 ft

A: Given query is to find the area of the trapezoid.

Q: az Find az and ду e = 5x 2² + sin(r + 2) – y?.

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Q: Question 6 Evaluate the double integral over the given region. S *+x4 - 3) dA, R: 0 sx s1,0 sy s2 15...

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Q: Find the arclength of y = 2x/2 on 1 < x < 3

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Q: Write an equivalent double integral with the order of integration reversed. dy dx dx dy dx dy ©SS ax...

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Q: Question 10 Determine whether the improper integral converges or diverges. dx 10 -9 A Diverges B) Co...

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Q: dy Find using implicit differentiation, for the equation a + = 11 is. da

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Q: Find the vector component of v = (4, – 1, 7) alongb = (1, 2, –2) and the vector component of v ortho...

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Q: The derivative of the function () y = In is: tan x,

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Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t2 from t = ...

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Q: er the following function and express the relationship between a small change in x and the correspon...

A: Topic:- application of derivatives

Q: dy Find using implicit differentiation, for the equation x° + y° = 10 is da %3D y7 y5 y5 o O O O

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Q: What is the amplitude and period of the function shown below? 5- 4- 3- 2- 1- -2 -1 -1 -3 2 3 4 6. -2...

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Q: Evaluate: sin ycos ydy. sinºy A siny +C 8. 6. sin y sinsy + C 8. sin°y sin'y + C 8. - 6. sin'y + C 8...

A: Here we need to solve the given integral .  

Q: A street light is at the top of a 19 ft tall pole. A woman 6 ft tall walks away from the pole with a...

A: This question can be solved using the concept of rate of change of physical quantities.

Q: The integral of t²In t with respect to t is; 13 A -(3ln t – 1) + C B none of the given choices -(31n...

A: Follow next step

Q: Find the area of the triangle with vertices P(1,6, –3), Q(0,0,0) and R(4, 6, 1). NOTE: Enter the era...

A: Solve for the area of triangle with vertices

Q: Find 2x dA over the region R = {(r, y) | 0<z< 4,0 < y < 6} by identifying it as the volume of a soli...

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Q: Determine the slope of the tangent line to the graph of ƒ (x) =- at the point(4, -4).

A: Use differentiation for finding the slope.

Q: A police car is located 60 feet to the side of a straight road. A red car is driving along the road ...

A: Solution: A police car is 60 feet to the side A red car 130 feet up the road  

Q: 3 is convergent or 24n-2 Determine whether the series Ć diveryent. It itis convergent, find its Sumi...

A: Topic:- sequence and series

Q: A circle is inside a square. The radius of the circle is increasing at a rate of 3 meters per hour a...

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Q: Find the equation of the circle shown. -7 -6 -5 -4 -3 -2 -2 -4- -5- of Write equation in standard fo...

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Q: DO NOT include spaces in between 10 characters. * Evaluate f'(-2) if ƒ(x) = x* – 5 + x-2 + 4x-4. %3D

A: Solve the function

Q: Sketch the region enclosed by y = 4x and y 4x2. Find the area of the region. %3D

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Q: Which of the following best describes the function below? S (x)={* -4 ifx<2 Wr-2 if2sx if 2<.x A. Co...

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Q: The ordinary differential equation x -y = x is a separable equation dy dx O False O True

A: Given query is to find that differential equation is separable or not.

Q: Evaluate: S,(3y6 + 8y* – 9y2)dy 2

A: Given query is to find the value of the integral.

Q: Find a function y(x) such that 5yy' = x and y(5) = 8. y =

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Q: Provide an equation of one of the common functions with multiple transformations. For example, f(x) ...

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