Let R be the region bounded by the lines y=0, x=2-y and the curve x = √y . i) Find the area of the region R. ii) Find the volume in π when the region R is revolved about the y-axis.

Q: 13. If a and b are positive real numbers, and let f(x)=x² +3x-5: a) Find f(-2). f(a+h)- f(a) b) Find...

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Q: II. Consider the region R below bounded by C1 : y = 2, C2 : y = 1 + 3 and C3 : 2y + x = 9. (1, 4) R ...

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Q: 13. If a and b are positive real numbers, and let f(x)=x² +3x-5: a) Find f(-2). f(a+h)- f(a) b) Find...

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Q: A. So20 V20 – h² dh | Which is the shape of the region being integrated? A. Triangle B. Part of a ci...

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Q: 1. Determine an equation for the graph of the polynomial function shown. y4 2 4+

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Q: Final answers. Interpret your solutions afterwards and provide some insights. 1. A pitcher of butter...

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Q: 3+3区

A: Use substitution

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A: Here  

Q: g(x) :|(1-/1- (a+1)²)da -x2 Solve for g(0) and g'(V2)

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Q: The graph of s() = 5 cos e is shown below. The range of this function is -7T

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Q: 4 r = - 5– sin 0

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Q: Which of the following differential equations is NOT separable? dy x + y dx dy 5(1 — у) dx dy = ex+y...

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Q: Use numerical evidence to estimate the value of the limit to at least 2 decimal places. - x – 20 lim...

A: Here we have to evaluate the limit of given function

Q: Think-Pair-Share. Directions: Evaluate the following limit. Answer it individually. (x²+ 5x+6Y 1. li...

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Q: 2. Draw any two from the following: i) Draw a Parabola by focus Directrix Method when the distance o...

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS, WE ARE ANSWERING ONLY FIRST QUESTION FOR YOU AS PE...

Q: Consider the equation below. f(x) = 4x3 + 3x2 - 6x + 3 (a) Give the intervals where f(x) is concave ...

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Q: What is the Taylor Series of f(x)=ex about x=0?

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Q: In a certain town in North America, the time of sunset for any day of the year can be found using th...

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Q: Question-4 If you are computing the average rate of change progressively over the intervals : [2,3] ...

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Q: Evaluate the following limits. sin- (e") 1. lim 2 V1- e20 1 1 x + sin 2. lim

A: On solving this we will get

Q: Given F(x) = ° (1– V1- (1+1)² ) d Evaluate F(0) and F'(V2).

A: The given integration is F(x)=∫-x201-1-(t+1)2dt ......................... (1)  By the Fundamental Th...

Q: Compute the difference quotient  f(x+h)-f(x)/h    , for the function below.                        ...

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Q: If f(x,y)3D 구+y, ry = , then fr(, y) is b.- (x² + y² )² a. C. 1² + y? (x² + y²)² 2r

A: Given query is to find partial derivative of the expression with respect to x.

Q: 3. The velocity function of a part. moving along a horizontal line is given by v(t) = In 2 - 24, whe...

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Q: Find the general antiderivative of f(x) = 9x + 18x-2 and check the answer by differentiating. (Expre...

A: NOTE: Refresh your page if you can't see any equations. . take integration 

Q: F(x) V16 – t² dt 4-x3 ||

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Q: 7. (-1,–x/6) 8. x2 - y? = 4

A: Given :7. ( -1, -π/6 )8. x2-y2=4

Q: Let R be the shaded region defined and bounded by the graphs of x2 C:y = 25 – x², C2:y : 5, and C3:y...

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Q: x² + 3x + 2 y' У(1) — 4 y – 2 -

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Q: 2. A particle is moving along a horizontal line such that its velocity is given by v(t) = 3t2 – 24t+...

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Q: Solve the inequality. Express the solutions in terms of intervals whenever possible: x — х — 2 2 x +...

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Q: Find an approximate value for 2√98.8

A: Let's find. 

Q: The value Daf of f (r, y, ) = e" cos y+el sin : at the point P(2, 1,0) where a is a unit vector in t...

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Q: Let R be the shaded region defined and bounded by the graphs of C:y = v25 – x², Cz:y =- 5, and C3: y...

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Q: The r- intercept of the surface 2r2 + 6y² – 3:² = 8 is equal to c.(+2, 0, 0) d. (±3, 0,0) a.(+v2,0,0...

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Q: apartment complex can rent all 150 of its one-bedroom apartments at a monthly rate of $450. For each...

A: Given query is to find find the rate of rent to maximize the rent collected.

Q: a + 15 da 12 — 6а + 13

A: The given integral,     ∫a+15a2-6a+13da

Q: Find all unit vectors perpendicular to (3, 1, 4) that make equal angles withj and k.

A: Here we have to find the unit vector. The solution is following. 

Q: Integrate tan -1 x dx without using integration by parts.

A: We will find the solution in the following step.

Q: Find the slope of the tangent line to the graph of f(x) = x · 2e'cos-'t dt at x = 1.

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Q: The vertices of a hyperbola are at (-5, -2) and (-5, 12), and the point (-5, 30) is one of its foci....

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Q: Suppose the function f(x) has a domain of all real numbers except  x = −8 . The first derivative of...

A: Given, f '(x) = −5(x − 4)/(x + 8)⁵ Therefore, f'(x)=0 For, x= 4 They are the required critical point...

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Q: Estimate the percentage change in the following function if x decreases by 1%, y decreases by 2%, an...

A: Topic = Algebra

Q: Newton’s method to find out maximum of

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Q: 9. r = 6+2 cos 0

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