8. Describe the type of indeterminate form. Evaluate the limit using L'Hôpital's Rule if necessary. sin 9x a. lim X-+0 Indeterminate form: Limit: b. lim (1+5x) X0+ 10 find the area of the region bounded by the graph of the function and the x-axis over the given interval. JE(18 2r2) (0 31

Q: 8 3. y2 = x and y² = 2 – x (Answer: S. U. ) 3 - -

A: Given: y2=x and y2=2-x   Now find the point of intersection between the given curves. y2=x,…

Q: Match the vector field with its graph. F(x, y) = yi y 1信 5 5 y 5 -6+ -5+

A:

Q: Write an integral that will give the area of the region in terms of dx (b) Write the integrals (do…

A:

Q: dy 1) dx y-x 2) y+x

A:

Q: Determine whether each of the following functions is (a) continuous (b) differentiable 3. f(x) = v2…

A: If function 'f' is differentiable at x=c the f'(c) is the slope of the tangent of the function at…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0<ts 1. (y – x) dx +…

A: Just I have used the given parametric representation of the curve C to change the given line…

Q: ||r'(t) × r"(t)|| ||r(t)||* Use the formula k(t) to find k(t). 13 r(t) = t²i + t'"j K(t) =

A: Find k(t).

Q: let f be the function given by f(x)=kx/(x^2+1), where k is a constant.  For what values of k, if…

A:

Q: 3. Find the area of the region inside the circler-3 sine and outside the limacon r= 2 - sine. Sketch…

A:

Q: E1 Fnd all of the Porst order partial derivatives Toll wing fanctions. a)そ= x+5y x Sin (y). b) fexy,…

A:

Q: Evaluate the triple iterated integral. r2 xyz dx dy dz

A:

Q: (4x-3) find dy/dх y = (2х-7)6

A:

Q: A certain rumor spreads through a community at the rate = 3y(1+y) , where y is the portion of the…

A:

Q: 5. Find the surface area when the curve C = {(x,y): 0 < x < 2, y² = 2 – x} about the x-axis.

A: Surface area

Q: /) Set up end eveluete fue defnite integrel for fue ared of tme Surfece fonmed by revoiving tme…

A: The graph y=x2, 2≤x≤8 revolving about x-axis

Q: 3z+1 Evaluate: S xp- 6z² -14x-12 ○ 륵m6z-21 + 흉mz + 6| +C O 음l미2z-6|+ n3z + 2| + C ○ f미3z-4|-3n 2z +…

A:

Q: Find the norm (or length) of v = <-2, 3)

A:

Q: QUESTION 10 If you have $51,000 in student loans at an interest rate of 3%, compounded monthly, what…

A: Solution:

Q: y"ーy=

A: Given problem:- Solve the following differential equation y'' -y=xe-x

Q: Determine whether the improper integral diverges or converges. In x converges O diverges Evaluate…

A: Here we have to determine whether the given improper integral diverges or converges.

Q: Answer the questions for the following polar equation. 3 r 3= 3+10cos0 (a) Identify the conic as a…

A:

Q: Evaluate the iterated integral. /4 y cos(x) dy dx 地

A:

Q: lim 3 1. x+00

A: To evaluate the given limit.limx→+∞1-3xx

Q: While standing on a bridge 30.0m above the ground, you drop a stone from rest. When the stone has…

A:

Q: Sketch the region R and evaluate the iterated integral F(x, y) dA. (1 - 2x + 8y) dy dx 2.0- 2.0 1.5…

A: A detailed solution is given below

Q: Evaluate the iterated integral. /3 6. y cos(x) dy dx

A: I=∫0π3∫09y cos x dy dx =∫0π3cos(x) ∫09y dy dx  =∫0π3 cos(x) y2209 dx  =∫0π3 cos(x)812 dx

Q: Part A) approximate the area under h(x)=x^2 from x=0 to x=2 using four rectangles and a left…

A:

Q: Find V · (V × F) if F(x, y, z) = 10 sin xi + 7 cos(9x – 10y)j + 3zk. V·(V × F)

A:

Q: - 9y" = 27 %3D

A:

Q: furt A)APproximate tue area unde hex)=X2 from x=0 to X=2u5ing four rectungles and X=0 a left and…

A:

Q: Calculate the maximum value of 10x + 23y subject to the constraints below: x + 2y < 14 X-y2 1 y 2 1…

A:

Q: (4) Evaluate each of the following indefinite integrals. r+2 (a) r² + 2r + 1 -dr (b) cos(2r) cos(r)…

A:

Q: Answer as directed. 1. it is convergent, evaluate it. Determine whether the improper integral is…

A:

Q: 1 Given that 1 > x" with convergence in (-1, 1), find the power series for with center 1- 9x4 n=0 0.…

A:

Q: h(x) = (5x-1 d) m(x) = (4x² – 9x} %3D

A: Product rule of differentiation: u·v' = u·v' + v·u'   ddxxn = n·xn-1 ddxf(x)n = n·f(x)n-1·f'(x)

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A: Given

Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti + tj dt

A:

Q: Inn 1 1 1 1 + 25 1 1 a) Σ-(-1)" (- b) 1+ 4 1 + 64 n-Inn. 9. 16 36 49

A:

Q: Determine whether the improper integral diverges or converges. 0. 8x xe dx -o. converges O diverges…

A:

Q: The sales function for a product is given by S(x) 124 + 37.8x? – 0.6x, wherex represents thousands…

A:

Q: 4. Find the length of the arc of the curve 6xy=yt +3 from the point where y - 1 to the point…

A:

Q: cos x sinx dx- 3 COS

A:

Q: Using an appropriate substitution, cos x-sin x the integral 3. dx equals: 0 cosx+sin x O none of…

A:

Q: Given (x) dx = F(x) dx = 7. 14 and %3D evaluate %3D (a) f(x) dx. (b) f(x) dx. (c) f(x) dx. 5. (d)…

A: Definite integration property

Q: 6) Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A:

Q: A ladder of length 4/3 metres is resting on a wall. The wall makes a 60-degree angle with the…

A:

Q: y2- 4y + 2x = 0, x = 2 and x-axis

A:

Q: S) Ffnd the nolyme of the Solid generatedd by revoluing the region boundeed by the graphs of the…

A:

Q: x* +x² 5. lim,-. e* +1

A:

Q: If the demand equation is D(x) = 180 - 6.3x and the supply equation is S(x) = 8.2x + 3, find the…

A: If the demand equation is D(x) = 180 - 6.3x and the supply equation is S(x) = 8.2x + 3, then we have…