Let y=f(x).Which of the following correctly defines dx [fk+Ax)-fw] a. lim Ax+xL Ax Ob. lim Ax+x k-Ax)-Fw)] Ax Oc lim Ar-oL Ax Od. lim Ax-OL fk-A)-f)] Ax

Q: メ +) メ +2 3. 2. メナ 3 メナ」 メト2 メ + 3

A: To find for what values of x determinant is 0.

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

A: Let's find.

Q: Q2) Convert the polar function r tan20 to cartesian.

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Q: Find the volume of the solid formed by revolving the region enclosed by the closed curve 4x² + 9y² =…

A: As per given  We have to determine volume of solid

Q: sequence

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Q: A line is drawn through the point (6,4,2) perpendicular to the yz- plane. Find the coordinates of…

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Q: 220° 12 сm 70° X =

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Q: Find an equation of the plane that is parallel to the plane x + 2y – 4z + 16 = 0 and contains the…

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Q: Q2) Convert the polar functionr= tan20 to cartesian.

A:

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 6z + 18 =…

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Q: 8. (5x'-4x +8x) dx

A: Topic = Integration As per guidelines , At a time only one question can be answered out of different…

Q: Question Approximate the local minimum value of the function given below. Use Newton's method with…

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Q: Consider the region bounded by the curve v= x2 – 1 and the x - axis over the interval [0,3]. Find…

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Q: 24. y' + y = -x/y

A: We have to find the solution of the given differential equation.   According to our guidelines we…

Q: Which of the following is the Taylor series expansion of the function -x2 with center at 0. f (x)=e…

A: Given problem:-

Q: -6x-'dx

A:

Q: Evaluate the following double integral over the region R. 7 x-y') dA; R= {(x,y): 0<xS1, -1sys1}…

A: Here we have to evaluate the given double integral over the region R .

Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

A:

Q: What is 2x4

A:

Q: 4 r4-y Evaluate triple integral , S S dz dy dx -2

A: We have to evaluate the triple integral  ∫-22∫x24∫04-ydz dy dx.

Q: Find the points on the curve y= (x-1)(x -4) where the tangent line is parallel to y= -4x, O (3, 10)…

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Q: Find f"(2) if Ax) %3D x² - 3* 08 O -7 4 O 2

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Q: Differentiate the following function and factor fully. g(x) = (2x – 1)*(2 – 3x)“ |

A:

Q: Find the area of the band cut from the paraboloid x² + y² – z = 0 by the planes z = 2 and z = 6.…

A: To find the area of the band cut from praboloid.

Q: g"(x) sin(x- 1) X-1 -4 13 h(x) = kr -8x+ 6, -1 10 4e-6-x+5, x>3 8 -1 (E) Find all x value(s) on the…

A: Given

Q: g(x) - tan(x)

A: The functions given are fx=x,gx=tanx. Formula used: Newton's Formula xn+1=xn-fxnf'xn

Q: H.w Pind the ro.t when [!,3} by Disection?

A: We have to find the root using Bisection method.

Q: ind the point of intersection (xo, yo, zo) of the lines given as: L: x = 2 + t, y= 4+5t, z = 5 +t L:…

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Q: Find (a) if fx) = /x-a+1.

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Q: Evaluate the following integral using Trigonometric Substitutions Method: п 2. y = 1- x dx

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Q: Q4) Evaluate the following integral using Trigonometric Substitutions Method: 2 y = - x dx

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Q: e-2 1 Evaluate: e-3 xInx Oc -In 6 O d. In 6 2/3

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Q: Water is pouring into a swimming pool. After t hours, there are t + sqrt(t) gallons in the pool. At…

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

A: The given problem is solved below in detail.

Q: EXAMPLE 3.1.1 Find the equation of the tangent line to the graph of f() = x² at z = 2 . Solution m =…

A: We have to find the equation of tangent.

Q: Question Using Rolle's theorem for the following function, find all values c in the given interval…

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Q: 6.Find all the first partial derivatives of each function x² – y² c. f(x,y) ху с. = d. f(x,y)=e* cos…

A:

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: Evaluate r(g(t)) using the Chain Rule: r(t) = (e', e", 4), g(t) = 2t + 5 %3D r(g(t)) = ( %3D

A:

Q: Consider z=e (*3+y2) Evaluate dx2 O (6r2+ 3x)e (*3+y2) (9x4+6x)e (x³+y²) (6x4+ 9x) e (x³+y²)

A: Topic = Derivative

Q: Find an equation of the sphere whose diameter is the line segment having endpoints at (6,2, –5)

A: To find the equation of sphere.

Q: Find y' if 4 cos x cos y = 3y. %3D

A: To find the derivative.

Q: Appraximate the critical numbers of the function shown in the graph. Determine whether the function…

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Q: Use a geometric series to represent each of the following functions as a power series about x 0.…

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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: Q3) Evaluate triple integral f, L(x - y?)dz dy dx.

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Q: Find the volume of the given solid over the indicated region of integration. f(x.y)%3D4X+5y+7;…

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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: (a).x = 61, y = - 4 + 7t O (r, y) = (0,4) + «(6, 7) ai + bj = 4j + 1(6i + 7j) O (1, y) = (6, 7) +…

A: topic - equation of a line

Q: Determine whether the line and plane intersect; if so, find the coordinates of the intersection. (a)…

A: