1.) Sand hole conical pile altitude always 1 4 of increasing when the 14 pouring from a the conical at on the rate of 25 the ground. If the diameter of pile is m³/min is forming has an and conical formation the base, how fast is the 5 m nigh? altitude

Q: Use integration by parts to find the indefinite integral. (Use C for the constant of integration.…

A: Note: ln(a×b)=ln(a)×ln(b)....(i) ln(an)=n×ln(an) ..........(ii)

Q: (B): If A = 2i +3j - 4k; B = 3i - 4j+5k and C = i + j - k, find: (iii)A. (B+C)and (A + B).C (iv)…

A:

Q: Transform the given differential equation into an equivalent system of first-order differential…

A: Using substitution and differentiation,

Q: Suppose the following: [ f(x)dx = 36, "f(x)dx = 12, f" f(x)dx = 12, [²9(x)dx = 24, and h(x): =…

A:

Q: Q2: Solve the following integrals: (1) f 7x²+14x+15 (x²+3)(x+7) dx ; (2) f sin x+cos x dx sin³ x…

A: We will use partial fraction to solve the first part of the question.

Q: (12) Find the derivative of the function Y = cos (a³ + x³)

A:

Q: Use the figure below to find the exact value of the trigonometric function of angle A. sin(A) 00 7 A

A:

Q: At what rate is the angle between a clock's minute and hour hands changing at 7 o'clock in the…

A: To find: Rate of change of angle between a clock's minute and hour hand at 7 AM. In other words, the…

Q: Use L'Hopital's to determine the limit. lim Oo O1 ○ -1 enx ~|-1 as x approaches co

A: This question can be solved using the concept of L' Hopital's Rule and derivatives.

Q: A rectangular field is to have an area of 500 m². a. Write the perimeter, P, of the field as a…

A: The solution is given below

Q: 2 x²log₂ (x) dx S

A: Please show complete solution. (Use integration by parts)

Q: 2. Approximate 64.1 by using linearization and use a calculator to compute the percentage error.

A: Given :64.13

Q: 34. dx = x³+4x² + 5x - 1 is given. What is ƒ(1)? A.-7 B.3 C.-2 D. 16 35. Evaluate the integral f(x²…

A: 34) The integration of the integral is f(x)/x2=x3+4x2+5x-1.  35) The given integral is…

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 (1) limx-o[: 1-cos x 2 sin²x (2)…

A: We have to find the limit using L Hospital rule.

Q: Find each of the following for f(x) = 6x² - 6x +6. (A) f(x+h) (B) f(x+h)-f(x) (C) f(x+h)-f(x) h

A: In this question we have to find the following given parts in the question.

Q: Q4: Answer two only: 2 1 -1 (A): I A=2 -2 Find AB and AC : - 1²/2 3 11 -2 -2 and 2 -- }

A:

Q: The radius of a right circular cone is increasing at the rate of 6cm/sec while  its altitude is…

A:

Q: Q1: Fill in the blanks for the following statements (chose five only) 4n 1. lim-00 2n+1 2. log10 (3x…

A: Authoring guidelines: As per the authoring guidelines, we can solve only the first three parts of…

Q: Use the disk method to find the volume of the solid of revolution generated by rotating the region…

A:

Q: Q5: Find d for the following functions: dx (1) In(x - y) = xy + y³ ; (2) y = tan³ √cot(7x) ;

A: We can solve the answers as below by finding the derivatives.

Q: Q5: Find for the following functions: dx (1) In(x - y) = xy + y³;

A: We have to find the dydx of the given function.

Q: Use the formula for instantaneous rate of change, approximating the limit by using smaller and…

A:

Q: Sketch the function. v(x) = 0.2(x-3)²(x+2)³

A: We can answer the question as below.

Q: Find all the zeros. Write the answer in exact form. q(x)=x²-₁ -7x+14x-6 If there is more than one…

A:

Q: Q3/ A. For the following function f(x). Find: f(x) = x² + 1 i. ii. iii. The slope of the f(x) by…

A: Given function, f(x)=x2+1 Aim: To find slope of f(x) Therefore differentiate w.r.t.x Therefore…

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x - sin²x

A:

Q: 18. Assume that f"(x) = (x + 2)²(x-2)(x - 3)(x - 5)³. Find x-value(s) for all inflection point (s).

A: If sign of f''(x) changes when we move from left to the right of x=a then x=a is known as the point…

Q: Consider the graph of the function f(x) given on the next page, which consists of line segments and…

A:

Q: Q1/ Solve the following differential Equations. 1- (1+x2)dy-xy dx = 0

A: To solve the differential equation.

Q: If you were to use a substitution of u = 4x³ - 2 to evaluate the definite integral below, what would…

A:

Q: The graph of y = f(x) is shown. Use the graph to answer the question. Find lim x-(-1)- O-2, -7 O-7,…

A:

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x 2…

A:

Q: 2 x³ dx -6 √x²-9 Evaluate O44√3 24√/3 34√5 34√3

A:

Q: 9. Find the equation of the curve whose y" e*. = - cos x + 6x + 4 with horizontal tangent at the…

A:

Q: Determine whether the improper integral diverges or converges. 16 1 √√√x dx converges diverges…

A:

Q: Find the radius of convergence for: 6nxn n! n=1

A:

Q: + 2x)² 4x +2

A:

Q: The vector v and it's initial point is given find terminal point v=, initial point (-7,-8)

A: In this question we have to find terminal point.

Q: Q3 (A): By using "L' Hopital rales "; Find the limits of: (1) tim-al-ca (2) lim, x(tan"¹x-x)

A:

Q: find the distance between point (-1,1,3) and the plane 5x-5y+3z=25

A:

Q: LI) Prove that (3

A:

Q: Find the Taylor or McLaurin series for the following functions f(x) = ln(1+x), a = 0

A: According to the question we need to find out the McLaurin series.

Q: Given the initial condition y(0) = 2, what i the particular solution of the equation √x - √ (x² +…

A:

Q: Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ≈ T₁(x) when x lies in…

A:

Q: Find the Taylor or McLaurin series for the following functions X f(x) = 1 + x², a=0

A:

Q: Cost, revenue, and profit are in dollars and x is the number of units. Suppose that the marginal…

A:

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (2) limx-o x-³ (tan-¹x - x)

A:

Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

A: Find determinant of coefficient Matrix  Then find delta x ,delta y, delta z

Q: Q3 :(A): By using "L' Hopital rules"; Find the limits of : 1 (1) lim,-ol1-cos x sin2x (2) lim,…

A: 3)1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0(tan-1x-x) /x3 Repost the next question.

Q: Evaluate the indefinite integral f7 sin v cos vdv =

A: Given ∫7sin6v cosv dvTo evaluate the integral: