Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Math Expert


Home >> Math

1. Evaluate the given limits, showing all working:

27_mathmatics eqution.jpg


2. Using first principles (i.e. the method used in ex 1, Washington 2009, Section 23.3 – Using definition to find derivative) find the derivative of each function and then evaluate the slope of the tangent line at the given point.

a). y = 12x2 - x3; (1, 11)

b). y = x/x - 1; (-3, 3/4)

3. The cross section of a hill can be approximated by the curve of y = 0.3x – 0. 00003x3 from x = 0 to x = 100 m. The top of the hill is level. How high is the hill?

4. A rectangular solid block of ice is melting such that the height is always twice the edge of the square base. Find the expression for the instantaneous rate of change of surface area A with respect to the edge of the base e.

 5. a) During each cycle, the vertical displacement s of the end of a robot arm is given by s = (t2 - 6t)(2t2 - t + 1) where t is the time. Using the product rule find the expression for the instantaneous velocity of the end of the robot arm. 

b) The amount n (in g) of a compound formed during a chemical change is n = 8t/2t2 + 3, where t is the time (in s). Find dn/dt for t = 3.0 s using the quotient rule.

6. The displacement s (in m) of an object as a function of time t (in s) is given by s = 3 √4 +9t
Using the Chain Rule find the values for:

i) The initial velocity.
ii) The velocity at t = 3 s.
iii) The initial acceleration.
iv) The acceleration at t = 3 s.

7.  a) A lens is described by the ellipse x2 - xy + y2 = 7 Use implicit differentiation to find the slope of a light ray tangent to the lens at  (1, −2 ).

b) Find the derivative of  x sec y - 2y = 2sin x cos x= −  without using a calculator.
 
b) Differentiate y = In(2x - 1/1 + x2)  without using a calculator.

8. For each of the following find:

i) The gradient of the graph at a given point
ii) The equation of the tangent line at that point
iii) The equation of the normal line at that point

a) y = 4x3 at the point (2, 32)

b) y = 1/2x at x = 1/4

9. a)  The distance d that can be seen from horizon to horizon from an airplane  varies directly as the square root of the altitude h of the airplane. If d = 213 km for h = 3950 m, find d for h = 5250 m.

b) The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. If V = 250 cm3when T = 200°

C and P = 130 kPa, what is the volume when T = 170°C and P = 130 kPa?

c) The acceleration of gravity g on a satellite in orbit around the earth varies inversely as the square of its distance r from the centre of the earth. If g = 8.7 m/s2 for a satellite at an altitude of 400 km above the surface of the earth, find g if it is 1000 km above the surface. The radius of the earth is 6.4* 106 m.

10. The time t required to test a computer memory unit is directly proportional to the square of the number n of memory cells in the unit. For a particular type of unit, n = 6400 for t = 25.0 s. Find the instantaneous rate of change of t with respect to n for this type of unit for n = 8000.

Math, Academics

  • Category:- Math
  • Reference No.:- M91049
  • Price:- $40

Guranteed 36 Hours Delivery, In Price:- $40

Have any Question? 


Related Questions in Math

Your financial situation and plansreflect on all that you

Your Financial Situation and Plans Reflect on all that you have learned in this course. Summarize your financial situation and plans. Be sure to include plans for budgeting, saving, debt and credit, taxes and insurance, ...

The annual rainfall in inches in a certain region is

The annual rainfall (in inches) in a certain region is normally distributed with mean? and variance 16. a) Over the years,it is found that the probability is 0.02 that the annual rainfall is less than 32 inches. Find the ...

What is the icd-9-cm describe at least one of the

What is the ICD-9-CM? Describe at least one of the outpatient coding guidelines listed in your text. What is the CPT? What symbols are used throughout the CPT coding book? Why are they used?

Suppose the set f of functions for a framework are all of

Suppose the set F of functions for a framework are all of gen-kill form. That is, the domain V is the power set of some set, and f (x) = G [ (x K) for some sets G and K. Prove that if the meet operator is either (a) unio ...

1 prove that if s is a finite set then s is a convex and

1. Prove that if S is a finite set then (S) is a convex and compact set. 2. Let A ⊆ R n and B ⊆ R m be two compact sets. Prove that the product set A × B ⊆ R n+m is a compact set. 3. Let A ⊆ R n and B ⊆ R m be two convex ...

Find the x- and y-intercepts of the line represented by the

Find the x- and y-intercepts of the line represented by the equation below. Plot both intercepts on a coordinate system and draw the line through them. 10x + 3y = 15

Suppose we have a cyclic data-dependence graph with nodes a

Suppose we have a cyclic data-dependence graph with nodes a, b, c, and d. There are edges from a to b and from c to d with label h0; 1i and there are edges from b to c and from d to a with label h1; 1i. There are no othe ...

Think of a recent event in the news where an ethical issue

Think of a recent event in the news where an ethical issue or social responsibility was highlighted. Describe the event, and share your thoughts on how it was handled by the individual or business.

Think of all issues that you considered in taking a

Think of all issues that you considered in taking a position or, if you aren't sure what your position is, what additional information do you need?

This week you have studied the graphs of rational functions

This week you have studied the graphs of rational functions and in particular asymptotes. In photography fixed focal length means that the focal length is not adjustable. Photographers are unable to zoom in and out on a ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen