Find the volume bounded by the paraboloid z = 1+ 3x? + 3y? and the plane z = 16 in the first octant.

Q: 1. Consider the region bounded by y = x and y = Vx, shown below. Find the volume of the solid obtain...

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Q: Find Homogeneous DE y'-ay=0

A: Given that: y'-ay=0

Q: Find the inverse Laplace Transform for Cari Songsangan Tranformasi Laplace untuk 1+(s-2)2 F(s) =5-2)...

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Q: A. Evaluate the following integrals by substitution. 1. fx(2x2 + 3)%dx x5 2. S; dx (x6-8)2 3. Sx V1-...

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Q: Let f(x) = sin(x) and g(x) = x². Find (fo g)' (x). (2æ)cos(x²) O (-2x)cos(x²) 2sin(x)cos(x) 2xcos(x)

A: Topic = Functions

Q: The function f(x) = 6x In(1 + x) is represented as a power series f(x) = E > Cnt". n=0 Find the spec...

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Q: Sketch a possible graph of a function that satisfies the given conditions. f(-1) = -7; lim f(x) = -2...

A: Given that f(-1) = -7. Therefore (-1,7) is a point on the graph .when x tends to -1 from the left si...

Q: 1 R(t) = 2 sin(t) – 4 cos(1)

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Q: Continuity of Functions on an Interval Determine if the given function is continuous on each of the ...

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Q: Examine the following functions for maxima-minima and trace the curve a. Y=x* + 1 a?x b. Y= a² –x²

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Q: (D² – 2D + 1) y = e*/x3

A: Given ,(D2-2D+1)y=exx3The A.E. is, m2-2m+1=0(m+1)(m+1)=0⇒m+1=0 or m-1=0⇒m=-1,-1Therefore C.F.=(C1+C2...

Q: C 1000 A В

A:  We know that law of sine is : SinA/a = SinB/b = SinC/c. Here A,B,C are angle of triangle and a,b,c ...

Q: Calculate and at the points (7,41, 1) and (7,41, –1), where z is defined implicity by the equation z...

A: Given the equation z4 + z2x2 - y - 9 = 0

Q: Find the volume formed by rotating the region enclosed by: x = 7.8y and y = x with y > 0 about the y...

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Q: x* + x³ + x² – x + 1 x(x² + 1)²

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Q: a. What is the bridge's height above the water? feet Preview b. How many seconds after being thrown ...

A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost oth...

Q: Find all the local maxima, local minima, and saddle points of the given function. f(x.y) = x? + xy +...

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Q: A volume is described as follows: 1. the base is the region bounded by æ = - y? + 10y + 95 and æ = y...

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Q: Find the endings for the following functions zX-5 3 @ lim - V-X-2 X -3 X +3 a lim 2- x* 1.

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Q: Write as a decimal. (Type a decimal.)

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Q: Find all the local maxima, local minima, and saddle points of the given function. f(x,y) = 2x2 +3xy ...

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Q: 55-68, evaluate the sine, cosine, and tar of the angle without using a calculator. 58. 675° 2n 64. 3

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Q: Evaluate the integral. | 8xex dx

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Q: The measure of an angle in standard position is given. Find two positive angles and two negative ang...

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Q: For the function f(x) given below, evaluate lim f(z) and lim f(r). f(z) = 6r 673

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Q: For the function, find the following. X + 1 2x (a) f"(x) 242 (b) f"(3) = 2/3 ||

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Q: Find numbers a and b, or k, so that f is continuous at every point. 3x+ 9, if x<-6 f(x) = { kx+ 6, i...

A: Hair we are given that the function is continuous at every point. we use the concept of limit for fi...

Q: n (n+1) (2n +1) 2. Find the sum (k+4)2, hint use use this formula and subtract out the 1, 2 ,3, and ...

A: Explanation of the answer is as follows

Q: Forms of Summation Notation 6. Square of the sum of variables: Ex; =(x, +x, +...+x,)? Example Evalua...

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Q: Integrate the function. S dt o. O. V6-R+ sin'1 6t + C 6t o. + C 612 o. 6t 16-12

A: We can find the integral as below.

Q: 1 n = 2

A: Telescoping series are series in which all but the first and last term cancel out.

Q: Given the first-order differential equation as below: (x² +3y +5)dx + (6xy + 6y +3)dy = 0 (ii) Calcu...

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Q: Continuity of Functions at a Point Determine if the given functions f(x) are continuous or not at th...

A: According to question,Given Function,fx = x2 + 2x +1 at x = 2

Q: Vx+3 4. f(x) = **3 f'(1) x-4

A: Given:- f(x) = √(x+3)/(x-4)  To find:- f'(1) 

Q: Using bisection method with [a1, b1] = [1,2] , estimate the root of x – 2 + Inx = 0 such that the to...

A: Given: fx=x-2+lnx a1, b1=1,2tolerance=fxi+1-fxi tolerance=0.01-------------------- Bisection Method:...

Q: * Limits of Polynomial, Rational, & Radical Functions Evaluate the given limits. 1. lim Vx+ 16 X-7

A: Here we have to evaluate the given limit.

Q: Integrate the functions in Exercises i to 23. 3x2 1. x° +1 1 V1+4x² (2=x)* +1 3x. V9 – 25x 1+2x 1-x ...

A: According to our guideline we can only answer first question and rest can be reposted.

Q: The Laplace Transform of

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Q: A tree on a hillside casts a shadow c = 230 ft down the hill. If the angle of inclination of the hil...

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Q: Find the volume of the solid generated by rotating the region bounded by y = sin°(x) and y = 0 betwe...

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Q: 4. (a) Prove the reduction formula: tan?n-1 (2r) _ [ tann-2 (2r) dr 4n- 2 tan" (2.r) dr (b) The redu...

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Q: Given the first-order differential equation as below: (x² +3y² +5)dx +(6xy + 6y + 3)dy = 0 (i) Ident...

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Q: yx+1 y=0, 0. 7 about the ras Siatch the region. Skatch the solid. and a typical disk or washer 10

A: Here, the given region is bounded by the curves: y=x+1, y=0, x=0, x=7

Q: Given the differential equation y" + 6y' 5e2 cos(9x) Find the Differential Operator for the Left Sid...

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Q: Test the series below for convergence using the ratio test. n+ 2 24n +1 n=1 The limit of the ratio t...

A: Given: ∑n=1∞ n+224n+1where f(n)= n+224n+1Ratio test : l=limn→∞ an+1anif l&lt;1 then the series is co...

Q: Some integrals might seem complicated. But they will simplify significantly if them in the right way...

A: Given that Fθ=∫cos3θ+sin2θ-3cosθsin3θ+3cos2θ+2sinθ-3dθ Evaluate the given integral

Q: 3x^2y^2+2x^3ydy/dx=0, Find differential equations'

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Q: To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an ang...

A: We can find the value of h as below.

Q: Find the x intercepts of the function f(x)=5|x-3|-3 (pleaes show steps)

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Q: Find the values of c that make f continuous everywhere: x? – c2 if x 8 smaller c = larger c = Use a...

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