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this is the link to differentitaing trignometric function chapter 6 in p2 and p3 i have a doubt in exercise 6a question number 6,question 7 and question 8 part a and part e.......
and also question 9 part b and f........................plzzzzzzzzzzzzzz reply asap...its just a few question.....plz attach scan!!
smzimran
minato112
celoth
plzzz help me asap
celoth help me with this first nowwwwwwwwwwwwwwwwwwwwplzzz 10,11,12 and 13th question solve and aTTACH AS A SCAN PLZZZZZZZZZZ if possibel or work it out here
plzzz 10,11,12 and 13th question solve and aTTACH AS A SCAN PLZZZZZZZZZZ if possibel or work it out here
and what about 11th question?no 10)
1st method: Chain rule:
Let u=a+x, du/dx=1
therefore, y=sin u, dy/du=cos u
by chain rule,
dy/dx
= dy/du x du/dx
= cos u x 1
= cos u
= cos (a+x)
2nd method: expansion:
sin(a+x) = (sin a)(cos x)+(cos a)(sin x)
dy/dx
= -(sin a)(sin x)+(cos a)(cos x)
= (cos a)(cos x)-(sin a)(sin x)
= cos (a+x)
the answer is same for both methods
Hi, I've got a bunch of questions ,I hope someone can help me
1) What is the common ratio of a geometric progression if the ratio of the sum to infinity to the sum 0f the first 7 terms is 128:127 ?
2)The 5th term is 2/81 and the sum of the 3rd and 4th term is 8/27 , Find the possible values of (a) r (b) the sum to infinity of this Gp .
3) The first three terms of a GP are 1 , a and b while the first three terms of an Ap are 1 , b and a where a is not equal b not equal 1,a) find the value of a and of b ,b) the sum of infinity of the GP .
*Gp:Geometric Progression .
Ap :Arithmetic progression .
Those are the answers of the questions
Answer:1)1/2
2)a) -1/4 or 1/3 ,b)2048/405 or 3 .
3)a)-1/2 , 1/4 , b) 2/3
I tried my best to reach the answers but i couldn't . So , please someone explain them for me
Question 2:
since Z = cos π/6 + i cos π/3
therefore, arg(Z) = π/6
or you can try to sketch this thing out on cartesian plane.
mod Z
= √ ( cos^2 π/6 + cos^2 π/3 )
= √ ( (√3 / 2)^2 + (1/2)^2 )
= 1
no 1)
to find r,
we know that the ratio:
Sum of infinity : Sum of 1st 7 terms = 128:127
127 x Sum of infinity = 128 x Sum of 1st 7 terms
127 x (a/1-r) = 128 x (a(1-r^7)/1-r)
by getting rid of (a/1-r) ,
127 = 128(1-r^7)
r^7
= 1 - 127/128
= 1/128
= (1/2)^7
therefore, r= 1/2
Hi, I've got a bunch of questions ,I hope someone can help me
1) What is the common ratio of a geometric progression if the ratio of the sum to infinity to the sum 0f the first 7 terms is 128:127 ?
2)The 5th term is 2/81 and the sum of the 3rd and 4th term is 8/27 , Find the possible values of (a) r (b) the sum to infinity of this Gp .
3) The first three terms of a GP are 1 , a and b while the first three terms of an Ap are 1 , b and a where a is not equal b not equal 1,a) find the value of a and of b ,b) the sum of infinity of the GP .
*Gp:Geometric Progression .
Ap :Arithmetic progression .
Those are the answers of the questions
Answer:1)1/2
2)a) -1/4 or 1/3 ,b)2048/405 or 3 .
3)a)-1/2 , 1/4 , b) 2/3
I tried my best to reach the answers but i couldn't . So , please someone explain them for me
Hi, I've got a bunch of questions ,I hope someone can help me
1) What is the common ratio of a geometric progression if the ratio of the sum to infinity to the sum 0f the first 7 terms is 128:127 ?
2)The 5th term is 2/81 and the sum of the 3rd and 4th term is 8/27 , Find the possible values of (a) r (b) the sum to infinity of this Gp .
3) The first three terms of a GP are 1 , a and b while the first three terms of an Ap are 1 , b and a where a is not equal b not equal 1,a) find the value of a and of b ,b) the sum of infinity of the GP .
*Gp:Geometric Progression .
Ap :Arithmetic progression .
Those are the answers of the questions
Answer:1)1/2
2)a) -1/4 or 1/3 ,b)2048/405 or 3 .
3)a)-1/2 , 1/4 , b) 2/3
I tried my best to reach the answers but i couldn't . So , please someone explain them for me
how to integrate tan2x with respect to x
change tan2x = sin2x/cos2x
And then we can use the substitution formula make cosx as u by i prefer not doing that cos it would be a nerve wrecking scenario!!change tan2x = sin2x/cos2x
no 3)
this question is interesting.
from the GP: 1, a, b
we can assume the ratio=a
because T2 = 1xa = a ,
then,
a x a = b
a^2 = b --- eq(1)
from the AP: 1, b, a
we can assume the difference is b-1,
since T2 = 1+(b-1) = b,
then,
b + (b-1) = a
2b-1 = a --- eq(2)
by putting eq(1) into eq(2) or vice versa,
you will be able to find a and b.
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