Show that for all n € N, one has 1 2√n+1 <√n+1-√n<; 2√ñ

Q: 1 2. Lim x0x 1 sin x

A: Given:      limx→0+1x-1sinx simplifying we get     =limx→0+sinx-xxsinx Apply L'Hospital's Rule:…

Q: dx 17.S (4x²-9)3/2

A:

Q: 4. 2x³y = y (g2 + 3z2)

A:

Q: If an object is dropped from a 150-foot-high building, its position (in feet above the ground) is…

A: Negative sign of the velocity is due to the downward movement of the body.

Q: Let (1) u(x, y) = xx vx, (2) u(x, y) = In(ex + ey). (3)

A: u(x,y)=xyyx u(x,y)=ln(ex+ey) Repost the next parts.

Q: Proving by Mathematical Induction A. 1. If P(2) = 1·3+2+4= 2(3) (11) 6 2. Prove that P(n) is true…

A:

Q: Find the area of the surface obtained by rotating the line y = 19x + 6 about the x - axis from the…

A: Area of surface is evaluated.

Q: Find the area of the surface obtained by rotating the line y the point (8, 158) to the point (17,…

A: The equation of the curve is given by y = 19x+6 To evaluate: The area of the surface obtained by…

Q: Rewrite the Cartesian equation r(0) = Enter theta for if needed. = 3 as a polar equation.

A: Topic = Geometry

Q: Q2:Expand using Maclourin series (1 - x 1-x² 2 ln(1 + x4) )? -

A: As per our guideline we are supposed to answer only one question of  multiple type of questions.…

Q: ?T f(t)=√ t` cosnt dt ((나) ans = 4 12 The easiest way to solve the integral so that the result is as…

A:

Q: Derive the following function 1 1. v = x²√x + √²²³√x 2. g(r) = (r²2r)er

A:

Q: Rewrite the Cartesian equation y = r(0) = = Enter theta for 0 if needed. 2x² as a polar equation.

A: In this question, we need to convert the given cartesian equation to polar equation.

Q: Question 19 Given f(x,y) = ex cos y, Evaluate fx(0,2) A) e² B 0 (C) -sin 2 D) cos 2

A: Topic = Derivative

Q: A bicycle with 24-inch diameter wheels is traveling at 16 mi/h.   Find the angular speed of the…

A: Given Problem:- A bicycle with 24-inch diameter wheels is traveling at 16 mi/h. Find the angular…

Q: For the given function f(x,y)=x²y³+3x³y, find a flay

A:

Q: 10. f3, (x²-1) dx

A:

Q: (a) Find the slope of the tangent line to the given polar curve at the point specified by the value…

A: We have to find the slope of the given polar curve at the point specified.

Q: 90 y 2 1980

A:

Q: 03: Fill in the blanks in the following: 1. If a (3,-2, 6) and b=(4,-1,-6) the axb = ******** .

A:

Q: (d) Let an = 6n²+ n-1 ntn and bn √n n+1' (i) Determine whether {an} is convergent or divergent.…

A: Given;  an=(6n2+n-1) /(n2+n)  bn=sqrt(n)/(n+1)

Q: 6. y = x Arccsc (¹)

A: we can find the y' as below

Q: Find the antiderivative F(x) of f(x) = 8(sec x)(sec x – 4 tan x).

A:

Q: Productivity-diminishing returns Suppose the pro- luctivity P of an individual worker (in number of…

A: We need to find out the number of training hours for the maximum rate of change in productivity.

Q: Q1:Discussion a continuity of the function f(x,y) sin x (x, y) = (0,0) f(x, y) = x (x, y) = (0,0)…

A: To find whether given function is continuous at (0,0) or not.

Q: f(x) = -x² + ax + b, x < 2 (-ax + 7, x ≥ 2

A: Here we have to find the value of a and b such that,  f(x)=-x2+ax+b, x&lt;2-ax+7, x≥2 is continuous…

Q: 2. Limx cosx x-o sinz sin²x

A: The given limit,    limx→0x2cosxsin212x

Q: Question R is the region bounded by the functions f(x) = + 1 and g(x) = - +7 over the interval [a,…

A:

Q: 1. Evaluate the given integral Q. Q - L. f.²² (y - 2x^²) dz dx dy Your answer

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: Derive the following function 6. y = 23x²

A: Given.

Q: dw Q11- express by using the chain rule: dt w = ln(x² + y² + z²) x = cost, y = sint, z = 4√t

A: We have to express dwdtby using the chain rule:

Q: Q1: Find the for the following functions: dy dx 1- y = e(x+In 5x) 2- y = cosh-¹ sin 2x 3- y = xsinh…

A: 1)y=ex+ln(5x) 2)y=cosh-1sin2x 3)y=xsinhx

Q: Q3: Fill in the blanks in the following: 1. If a=(3,-2, 6) and b =(4,-1,-6) the axb = ********* 2.…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: f' (æ) =Vx+, f(0)=2 f"(x) = 3x² 16x + 16, f'(0) = 1, ƒ(0)

A: Topic:- application of integration

Q: Evaluate x ds, where Cis с a. the straight line segment x = t, y = = 737₁1 3' b. the parabolic curve…

A:

Q: dy : Find the for the following functions: dx 1- y = e(x+ln 5x) 2- y = cosh-¹ sin 2x 3- y = xsinh x

A:

Q: (d) Given r(t) = (ln(t+1), t cos 2t, 2¹). (i) Find r'(t). (ii) Find parametric equations for the…

A:

Q: Find the integrals of the given in the picture

A:

Q: 5. sin(x + y) = y² cosx

A:

Q: Find the third Maclaurin polynomial to f(x) = e sinx

A: The Maclaurin series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+.... Where the center is at x=a=0…

Q: dx 20.5 x√4x²-49

A:

Q: Suppose a population of fruit flies changes at a rate of g(t) = -4e0.041, in flies per day. If the…

A: Here we have a population of fruit flies that changes at a rate of g(t)=-4e0.04t…

Q: solve the following problems. Draw the necessary figures for each. The area bounded by the parabola…

A: The area bounded by the parabola y2+x-2y=1, the x‐axis, and the line x=2, revolves about the x‐axis.…

Q: 3. 4. If =(-12, 4, 8) the position vector of u is.............

A:

Q: Assume that y is a differentiable function of r such that y² = x² + 4x sec y. Find y' by implicit…

A: implicit differentiation

Q: Q4:Evaluate 1) lim (1-²) x-0 \sin x

A:

Q: Consider the function f(x) = 4x² Identify the locations where f has transition points. (Give your…

A:

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A:

Q: answer the related questions. 7. ул y = G(x) 3 10 + N grap -2 -1 0 4 5 a) Find lim G(x). x-3+ b)…

A:

Q: Used Cramer's Rule to find the value of the variables (X,Y,Z) in the following equations x + 2y + 3z…

A: The objective is to find the value of the variable x, y, z by using crammer's rule.