A curve has the equation y 2tan x 1 where x is measured in radians a Show that the curve passes through the points (0, 1) and ( 4, 1) b Find the equations of the tangents and normals at each of these points ...

a To show that the curve passes through the points 0 1 and 4 1 we substitute the xvalues ...

A curve has the equation y = 2tan x 1 where x is measured in radians.

Question:

A curve has the equation y = 2tan x − 1 where x is measured in radians.

a. Show that the curve passes through the points (0, −1) and (π/4, 1).

b. Find the equations of the tangents and normals at each of these points.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Cambridge IGCSE And O Level Additional Mathematics

ISBN: 9781510421646

1st Edition

Authors: Val Hanrahan, Jeanette Powell

See More Books

Question Posted: Sep 03, 2021 01:32 AM

See More Questions

A curve has the equation y = 1.5x 3 3.5x 2 + 2x. a. Show that the curve passes through the points (0, 0) and (1, 0). b. Find the equations of the tangents and normals at each of these points. c....
A curve has the equation y = e x ln x. a. Sketch the curves y = e x and y = ln x on the same axes and explain why this implies that e x ln x is always positive. b. Show that the curve y = e x ln x...
A curve has the equation y = (x 3)(7 x). a. Find the gradient function dy/dx. b. Find the equation of the tangent at the point (6, 3). c. Find the equation of the normal at the point (6, 3). d....
At times we can generate a regression equation to explain outcomes. For example, an employees salary can often be explained by their pay grade, appraisal rating, education level, etc. What variables...
Using solubility rules, decide whether the following ionic solids are soluble or insoluble in water. If they are soluble, indicate what ions you would expect to be present in solution. a. (NH4)2SO4...
Intella, Inc. adopted the dollar-value retail LIFO method on January 1, 2006. The following data apply to the 4 subsequent years: In addition the following price indexes are available: January 1,...
Bergamo Bays computer system generated the following trial balance on December 31, 2019. The companys manager knows something is wrong with the trial balance because it does not show any balance for...
Bolster Foods' (BF) balance sheet shows a total of $25 million long-term debt with a coupon rate of 8.50%. The yield to maturity on this debt is 8.00%, and the debt has a total current market value...
5-year CDX NA IG index is quoted by a market maker as bid 160 bp, ask (offer) 165 bp. This index includes 125 North American investment-grade companies. Suppose you want $800,000 of protection for...
A 16-run fractional factorial experiment in 10 factors on sand-casting of engine manifolds was conducted by engineers at the Essex Aluminum Plant of the Ford Motor Company and described in the...
a. Find the stationary points of the function f(x) = x 2 (3x 2 2x 3) and distinguish between them. b. Sketch the curve y = f(x).
The graph of y = px + qx 2 passes through the point (3, 15). Its gradient at that point is 14. a. Find the values of p and q. b. Calculate the maximum value of y and state the value of x at which it...
Draw a free energy versus reaction progress diagram for a reaction that occurs in two steps with a relatively stable intermediate and in which the transition state for the second step is the...
Write out the form of the partial fraction decomposition of the function (see example). Do not determine the numerical values of the coefficients. x3 (a) x + 7x+6 9x+1 (b) (x + 1)3(x + 2) Submit...
You desire to make an 80% by weight vinyl acetate to 20% by weight styrene copolymer via free radical, emulsion polymerization. The r 1 and r 2 values for these monomers are 0.01 and 55,...
Q1)In a wheel and axle machine the diameters of the wheel and the axle are 450mm and 60mm respectively.The efficiency is 97%(0.97 per unit).When a body having a mass of 40kg is being lifted.Determine...
Smith & Chief Ltd. of Sydney, Australia, is a merchandising firm that is the sole distributor of a product that is increasing in popularity among Australian consumers. The company's income statements...
C. In lab, you measure the x & y components of a possible incompressible flow field as u = 2cxy; and where cand a are constants. v = c(a + x - y) 5. (04 pts) Short answer, what is necessary for the...
The accounting records of Nettle Distribution show the following assets and liabilities as of December 31, 2017 and 2018. Required 1. Prepare balance sheets for the business as of December 31, 2017...
Will the prediction interval always be wider than the estimation interval for the same value of the independent variable? Briefly explain.
The table shows experimental values of two variables x and y. It is known that x and y are related by the equation y = a/x + bx, where a and b are constants. a. Complete the following table. b. On a...
The table shows experimental values of the variables x and y. The variables are known to be related by the equation y = a b x where a and b are constants. a. Draw the graph of lg y against x. b. Use...
Variables x and y are related so that, when e y is plotted on the vertical axis and x 2 is plotted on the horizontal axis, a straight-line graph passing though the points (3, 4) and (8, 9) is...
Suppose the S&P 500 currently has a level of 960. One contract of S&P 500 index futures has a size of $250 S&P 500 index. You wish to hedge an $800,000-portfolio that has a beta of 1.2. (A)In order...
Exhibit 4.1 The balance sheet and income statement shown below are for Koski Inc. Note that the firm has no amortization charges, it does not lease any assets, none of its debt must be retired during...
Haley is 57 years of age. She is planning for future long-term care needs. She knows that yearly nursing home costs in her area are currently $69,000, with prices increased by 5 percent annually....

A curve has the equation y = 2tan x 1 where x is measured in radians.

Question:

Step by Step Answer:

a To show that the curve passes through the points 0 1 and 4 1 we substitute the xvalues ...View the full answer

Cambridge IGCSE And O Level Additional Mathematics

Students also viewed these Sciences questions