Check the continuity of the function f(x). Explain why f(x) is continuous or not. x+1 =,x <1 xV1-x f(x) = 2, x = 1 %3D x4+1 ,x > x2X > 1

Q: Find the 0lar eauatiDo for the curve represented by the given Cartesian euation.

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Q: Consider the function f(x) = 3 sin (). Construct the interpolation polynomial which interpolates the…

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Q: 3 5 8x 15 dx 5 x4 |

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Q: Consider --e +y?). 3+3² Evaluate dxdy

A: We have to find partial derivatives for the given function.

Q: Question Use the second derivative test to find the location of all local extrema in the interval…

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Q: given below, evaluate lim f(x) and lim x→-00 f(x) = -4x² + 2x +4 sin (9x) ses without bound, you…

A: We have to find the following conditions according to the given information

Q: Find the third derivative of f(1)= 2x(x -1)" Oa 18 b.14cos 13 OC16sim Od12

A: we all know that dxndx= nxn-1. and first derivative dfxdx=f'x and second derivative df'xdx=f''x and…

Q: Q4/ solve the equation by Newton -Raphson Method: F(x) = x* – 5x³ + 65 , start at x =2 , accuracy…

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Q: Q4) Find plane area inside the polar function r = 2 and outside polar function r = 2 sin (* + 0) in…

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Q: Solve the following differential equation by the method of Variation of Parameters: x" + 49x csc…

A: The given differential equation is;  x''+49x=csc2(7t).

Q: 5. In antidifferentiation, the formula J x" dx : + Cis valid if? (n+1) C. ne {0,1,2} A. nER 6. In…

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Q: Q2) Solve the D.E x²dy + (3xy- 1)dx 0

A: Let's find.

Q: Q5) Find volume of body bounded by z? + y? + x? = 9.

A: Let's find.

Q: Show that the lines L1 : x = 5 – t, y = 2t, z = 1+t and L2 : x = 1+ 2t, y = 3 – 4t, z = 5 – 2t are…

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Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

A: Here we have to use the trigonometric subsitution method.

Q: Evaluate the following limit: (x- 2)2 – 4 | lim If it does not exist enter DNE.

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Q: c(x)=2x2-7x; c(0)=4,000

A: answer is in next step

Q: nsider Evaluate дхду

A: Given,             z=ex3+y2To find : Evaluate ∂2z∂x∂y

Q: Consider the parametric curve defined by x=3+5t and y=1+31 Over which values of , does the curve has…

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Q: n(A U B) = 55, n(AN B) = 15, and n(B) = 35 %3D Find the value of x A 15 y

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Q: Evaluate the following integral using Partial Fractions Method: x3 + x2 y : dx x2 + x – 2

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Q: From Rogawski ET 2e section 10.3, exercise 5. Use the Integral Test to determine whether the…

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Q: Evaluate f s 2°ds О а. 2"(sin2 - 1) (In2)2 O b. 2(sln2 - 1) (In2)2 O C. 2* In2 O d. 25 In2

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Q: Evaluate the following integral using Trigonometric Substitutions Method: dx y = 9x2 + 16

A: We will use simple Integration rules to solve this question.

Q: Descibe he moton of a partice with position y= 5 sin t; y=2 cos t as t varies in the interval - T, 5…

A: To find the motion of particle.

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4 – y from above inside y = x? ,y = 4 .…

A: Given

Q: а. Consider the functions y = 2u² + 3u and u = x². Find dx b. Find the derivative of the function…

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Q: Q3) Evaluate triple integral , dz dy dx.

A: ∫-22∫x24∫04-ydz dy dx∫dz=zSubstitute the limits=4-y-0                              =4-y

Q: The height of a ball t seconds after it is thrown upward from a height of 5 feet and with an initial…

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Q: 1 lim X0-x23

A: Given,limx→ 0-1x23We know that,For x approaching 0 from the left, x&lt;0  ⇒   x23&lt;0The…

Q: Evaluate (s 2 ds Oa.2 sln2-1) (In2)2

A: ∫ s· 2sds=2ssln2-∫2sln2ds=2ssln2-2sln22Add a constant to the solution=2ssln2-2sln22+C

Q: Find the absolute extrema of the function on the closed interval. h(s) = [0, 2] S-3 minimum (s, h) =…

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Q: Find the value of t for which 1 V3x+1 O none of the choices 6 O 3 O 5 O 4

A: Here, given that: ∫1t13x+1dx=43

Q: Q2) Solve the D.E dy - (2x/1-y2)dx 0

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Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 6 Y 4 6. 10 10 8

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Q: Let a = 2i – 3j and b= 2j + 3k. Compute for the following: (a + b) · (a – b) None of the choices -8…

A: Here we have to find the dot product.

Q: Evaluate triple integral , S S dz dy dx. 4-y -2 Jx2 Jo

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Q: 4. Estimate the net area under the curve bounded by the x-axis from x = 1 to x = 7 with 12…

A: answer is in next step

Q: EValuate J s 2'as O a. 2*(sln2 – 1) (In2)2 O b.2(sln2 - 1) (In2)2 O C. 25 sp.7s (1 – Zu). + 1) In2 O…

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Q: Consider a continuous function f(x). The function has critical points at x = -7, x = -2, and x = 7.…

A: f(x) has critical points at x=-7 , -2 , 7Since f''(-7), f''(-2) is positive ⇒There is local minimum…

Q: 1. S(5x4 + 2x – 1)dx

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Q: At what rate is the distance between the planes changing? Step 1 Let s denote the distance in miles…

A: Topic:- geometry and application of derivatives

Q: 1 Evaluate: xInx In Oc -In 6 O d. In 6 l3.

A: The given problem is solved below in detail.

Q: 1. Find the indicated limit or state that is does not exist lim (3x'y- xy³) а. (x,y)→(1,3) b.…

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Q: A particle is moving in space and its position at time t is given by r(t) 4(cos t)i+ 4(sin t)j+ /²k,…

A: Given problem:-

Q: Question 18 Consider Evaluate O (9x4+6x)e (x3+y2) O (3x²+6x)e «³+y?) O (6x²+ 3x)e «³+y?) O (6r*+9x)e…

A: Topic = Derivative

Q: Use the first principles definition of the derivative to find f"(2) where Ax) = O a) 0.125 b) 4 c)…

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Q: Find the value of A which is defined as the angle between i+j and j+ k.

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Q: y = Vx* X

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