8. (a) Use the limit comparison test to determine whether the series converges. k=1 (b) Use the ratio test to determine whether the series , 4* converges. k=1 IM:

Q: 10 if f(x)= t +P, then %3D f'(X) = f'(-2)=

A:

Q: For what values of x do the tangents to the curves y = (1 +x')² and y = 2r6 have the same slope? X =…

A:

Q: rln 2 e2" sec-'(e²)dx 0.

A: Answer is in below steps.

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: Cha invests Php5,000 in an investment that earns 6% per annum. How many complete years does it take…

A: Given Cha invested(P)= Php5,000Rate of interest (R)=0.06Time (t)=?Amount (A)=Php 10,000We know that…

Q: 4. S cot?x dx

A:

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

A: Let's find.

Q: Find the Area bounded by the curves y² = x and x = 2y – y². %3D

A:

Q: I c exists in (0, 1) such that f(c) (1)- f(0) 1-0

A:

Q: Find an equation of the plane that passes through the points (1,5, 2), (3, 4, –2), and (-–5, 5, 1).…

A:

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

A:

Q: Find the AuRtaYe value of f(x) = x* on the intervai 2,67

A: answer is in next step

Q: QI) Evaluate the integral dx dy using polar coordinate

A: Solving

Q: Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not…

A:

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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: x² + 2y? + 3z² 18. lim (x, y, 2) →(0, 0, 0) x² + y² + z?

A: We have to find the limit by two ways method

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

A:

Q: Convert to an equation in rectangular coordinates. r = 4 csc (0) – sec (0) (Express numbers in exact…

A:

Q: A company produces two types of solar panels per year: x thousand of type A and y thousand of type…

A:

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

A:

Q: Question A 5-foot ladder is leaning against a wall. If we push the ladder toward the wall at a rate…

A: let x be the distance of bottom of ladder from the wall andy be the distance between top of the…

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

A: Here we have to solve the given differential equation x2dy+3xy-1dy=0 ............................…

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

A:

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: Q3) Evaluate triple integral f x - y²)dz dy dx.

A:

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

A:

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

A:

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

A:

Q: Find the average value of the function f(x)=e" on the interval (0,4) Da 3725 Ob 490 OC 745 Od 186 25

A:

Q: Find the two x-intercepts of the function f and show that f'(x) = 0 at some point between the two…

A:

Q: Which of the following limits has a value 0? In x I. lim II. lim X-0 e* Neither I nor II. O l only…

A:

Q: 18. Find the shaded area in the following figure. Assume that there are infinitely many squares and…

A: Area of Infinite shaded region Let Sk be the sum of area of each shaded regionthen…

Q: Evaluate triple integral f, SE Lx? - y?)dz dy dx.

A:

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

A:

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

A:

Q: 1 Find f'(-1) if Ax) = (2x + 1)², O-4 04 O-1

A: The given function,       fx=12x+12

Q: ト+ se=Atzメ

A:

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: QI) Evaluate the integral dx dy using polar coordinate

A:

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

A:

Q: The radius r of a sphere is increasing at a rate of 2 inches per minute. (a) Find the rate of change…

A:

Q: Sx³e** dx

A: To evaluate: ∫x3e4x dx

Q: Question You are stationary on the ground and are watching a bird fly horizontally towards you at a…

A:

Q: 5.Find all the first partial derivatives of each function f (x,y) =(2x– y)* а. 3/2 S(x, y)= (4x–…

A:

Q: sin x Let g(x) = 1 ot. Find the derivative d'(x). '2 1+t3 none of the choices cos X 1+ sin3x sin? x…

A:

Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A:

Q: Evaluate the following iterated integral. 2 16 15y dx dy 2.

A:

Q: el-vidx

A: