true or false: If a finite number of terms are added to a convergent series, then the new series is still convergent.

Q: Зх-1 13. f (x) = ;(-1,6] х2—7х-8

A:

Q: Average Rates of Change Use each graph to estimate the average rate of change of the percentage of n...

A: We need to find the average rate of change for the given graphs.  

Q: dx 4+ x² Use integration by parts. let u = x? dx 4+ x2 dv =

A:

Q: The slope of the tangent line to the curve y 2x at the point 2, 16) is:

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the functi...

Q: 14. Find the orthogonal trajectories of the family of curves 1 y =- (x + k)³ (a) y = (3x+ C)/7 (d) y...

A:

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x? + ...

A: Given equations are:  x2+y2-2ax=0x+y=2a   The bounded region is rotating about the line x=0.

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A:

Q: 3. 2- 1- ol 1 4 Let R be the region bounded by the graph of y = Va – 1, the horizontal line y = 2, a...

A: As shown taking the horizontal stripe x changes from 1 to y2+1 because  y=x-1⇒y2=x-1⇒x=y2+1

Q: Find the directional derivative of the fellowing functions at Point Po in direction of the Vector à ...

A:

Q: fm and n are odd integers, then so is m · n.

A: Given query is to find statement true or false.

Q: 2.

A: ∫x2ex dxBy integration by parts

Q: In a psychology experiment, the time t, in seconds, that it takes a rat to learn its way through a m...

A: Given density function of time t in second for a rat for its way through maze  f(t)=0.04 e-0.04t

Q: dx Evaluate J 2/4+x²

A:    ∫1x24+x2dxLet x=2 tan u.=∫secu4tan2udu=14·∫secutan2udu=14·∫cosusin2uduLet v=sin u.=14·∫1v2dv=14-1...

Q: he points A(1,-2,4) and B(2,-4,1) cach make direction vectors with the point (Xo.Yo, Zo). The point ...

A: The Parametric equations of the line are the components of the vector equation , and have the form  ...

Q: 2. Evaluate. th fallowing.integrals.a.fte..seueo.ing.the arder.af.integratren. dyd x Ans..In7)4 .0.t...

A:

Q: | xf(x2) dx. If f is continuous and f(x) dx = 4, find

A:

Q: Find the equation of the tangent to the graph at the indicated point. f(x) = x2 – 5x; a = -2 y =

A:

Q: x² + ax + 2bx + 2ab + 2x² – ax² + 6bx² dx x* + ax² + 2bx² + 2abx²

A:

Q: Sketch. the.region.cf.integratizin.and.evaluabe. thaw .. fallowing. integrals a ..... in2 Ins 2X-년 A...

A:

Q: 2. Find the derivative of y = (5x³ + 2 x)tanx. %3D

A:

Q: 8. What is dx (x2+8)3

A:

Q: 2 A spherical snowball is being made so that its volume is increasing at the rate of 8ft³ jmin/ Find...

A: This is a problem related to the volume of the spherical snow ball and change in rate. By using conc...

Q: Find the vector component of v = (4, - 1, 7) along b = (3, 6, -6) and the vector component of v orth...

A: This question is based on Use of Dot product and cross product.

Q: 13 8 cos 37 + i sin 8 |10 + i sin 16 Cos 16

A:

Q: Find the solution of the following Differential Equations 2) y"+2y'+y x 4) y"+y=-30sin(4x)

A:

Q: A solution composed of 50% ethanol (EŁOH), 10% methanol (MEOH), and 40% water (H2O) is fed at the ra...

A:

Q: Consider the two functions fx) = 5x + 5 and g(x) = 5x - 5. a. Determine the instantaneous rate of ch...

A:

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² + ...

A: Given equations are:  x2+y2-2ax=0x+y=2a

Q: 1. What is the slope of the tangent line to the curve f(x) = 5a2 - e* - e, at a = -1? (A) –10 e (B) ...

A:

Q: xydx – (x² + 2y²)dy = 0 ||

A:

Q: Find the gradient of the function and the maximum value of the directional derivative at the indicat...

A: Gradient of a function f(x,y,z) is given by,          grad(f(x,y,z))=i∂∂x+j∂∂y+k∂∂zf(x,y,z) Maximu...

Q: If m and n are odd integers, then so is m · n.

A: We will use the definition of an odd integer to prove this statement.

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. ...

A: The graph is shown below:

Q: 2. Determine f'(-1) for the function f(æ) = (x" – 2r° + 1)(x³ + æ -- 2). 8 (B) 12 (C) 14 (D) -4 (E) ...

A:

Q: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular windo...

A:

Q: dy then dx sin x If y = 1+ cos x ||

A:

Q: Determine whether the series converges or diverges. ∞ ∑                                         2...

A: Given query is to find series converges or diverges.

Q: 4x Estimate the error in the quadratic approximation of f(x,y) = e sin y at the origin over the regi...

A:

Q: Determine whether the series converges or diverges. +00 2n + 2 Vn3 + n2 + n n=1

A: Given query is to find series converges or diverges

Q: Evaluate the integral using the following values. 6 dx = 260, х dx %3D 10, dx = 2 4 4 "x³ dx

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

Q: find d^2y/dx^2: y^3=4x^6

A:

Q: Find the area of the region enclosed by the graphs of 1 1 1 – 16æ²' Y = 0, x = 0, and æ NOTE: Enter ...

A:

Q: 6. Given f(x) =x° and g(x) = x, sketch h(x) = f(g(x)).

A: As you mention question no. 6 solved

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 4(x² – ...

A:

Q: Find unit vectors that satisfy the stated conditions.

A:

Q: How many positive integer solutions (zero is not allowed) to r+y =42?

A:

Q: Find the particular solution of the differential equation that satisfies the initial condition. f'(x...

A: I am attaching image so that you understand each and every step.

Q: Assume that w = f(s3 + t?) and f'(x) = ex. Find dw dw and at ds dw at dw

A:

Q: 3. a) Find polar coordinates (r, 0) of the point (1, -/3), where r> 0 and 0 <0 < 2 p2 = x² + y?, tan...

A:

Q: Find the volume generated by revolving bout the line y = -1 the area bounded by (х — 2) %3D 4(у + 2)...

A: Given that the area is bounded by x-22=4y+2 and y=-1.It is required to find volume generated by revo...