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Integration of tangent cubed of x?
Find I = ∫ tan³ x dx. The solution is: I = ½ tan² x - log cos x. * * * Here is how we can obtain this result: First, let t = tan x, s = sin x, and c = cos x; then, dI = t³ dx, ds = c dx, dc = -s dx, and dt = (1 + t²) dx; and, of course, t = s / c. By algebra, t³ = t(t² + 1) - t; thus, we have dI = t³ dx = t(t² + 1) dx - t dx = t dt - t dx. Now, d (t²) = 2t dt; thus, t dt = ½ d(t²). On the other hand, we have d log c = dc / c = -s dx / c = -t dx; thus, t dx = -d log c. Combining these results, we have dI = t dt - t dx = ½ d(t²) - d log c. This integrates readily, giving I = ½ t² - log c, which is the solution we sought. * * * We may check our result, by differentiating back: dt / dx = 1 + t²; and d(t²) / dt = 2t; thus, (d/dx)(t²) = 2t dt / dx = 2t (1 + t²). Also, we have d log c / dc = 1 / c; and dc / dx = -s; whence, (d/dx)(log c) = (dc / dx) / c = -s / c = -t. Then, dI / dx = ½ (d/dx)(t²) - (d/dx)(log c) = t (1 + t²) - t = t + t³ - t = t³, re-assuring us that we have integrated correctly.
How write a c program to generate fibinocis series upto n turms?
int f1=1, f2=1, c=2; do { t=f1+f2; printf("%d\t",t); f1=f2; f2=t; c=c+1; }while(c
Derive using inference given conclusion if g then c premise one if g or h then s and t premise two if t or u then c and d?
g => (g or h) => (s and t) => t => (t or u) => (c and d) => c.We are given premises:# (g or h) -> (s and t) # (t or u) -> (c and d) We would like to derive g -> c.If we assume g (the antecedent in the conclusion) we have the following derivation: # g (assumption) # g or h(weakening) # s and t (premise 1 (modus ponens)) # t(weakening) # t or u (weakening) # c and d (premise 2 (modus ponens)) # c (weakening)So, assuming g we can derive c, i.e. g -> c
How does a Jacobson's organ function?
1. B 2. A 3. C 4. D American School Of Corr. Biology Examination 8, question 5. The snake has a tongue which is known as the jacobson's organ. Through this the snake smells the air in the environment and finds its prey in the surroundings. 6. t 7. t 8. t 9. f 10. f 11. t 12. t 13. t 14. t 15. t 16. t 17. t 18. f 19. f 20. f 21 d 22 c 23 c 24 a 25.c 26 c 27 c 28 b 29 d 30 b 31 d 32 b 33 a 34 d
How does a Organism function?
1. B 2. A 3. C 4. D American School Of Corr. Biology Examination 8, question 5. The snake has a tongue which is known as the jacobson's organ. Through this the snake smells the air in the environment and finds its prey in the surroundings. 6. t 7. t 8. t 9. f 10. f 11. t 12. t 13. t 14. t 15. t 16. t 17. t 18. f 19. f 20. f 21 d 22 c 23 c 24 a 25.c 26 c 27 c 28 b 29 d 30 b 31 d 32 b 33 a 34 d
How does organ function?
1. B 2. A 3. C 4. D American School Of Corr. Biology Examination 8, question 5. The snake has a tongue which is known as the jacobson's organ. Through this the snake smells the air in the environment and finds its prey in the surroundings. 6. t 7. t 8. t 9. f 10. f 11. t 12. t 13. t 14. t 15. t 16. t 17. t 18. f 19. f 20. f 21 d 22 c 23 c 24 a 25.c 26 c 27 c 28 b 29 d 30 b 31 d 32 b 33 a 34 d
C orogram for Fibonacci series?
#include<stdio.h> #include<conio.h> void main() { printf("The first 20numbers of Fibonacci series are:"); int a=0, b=1, c, n=2; printf("%d \t, %d", &a, &b); while(n<20) { c=a+b; printf("\t %d", &c); a=b; b=c; n++; } getch(); }
What are the piano chords to nicest thing by Kate Nash?
T| 3|-d-f-d-f-d-f-c-f-c-f-c-f----f----f----f-a-f-a-f-a------------------| A| 2|-------------------------A----A----A--------------------------------------| B| and then again with d and so on ...
What comes nest in this series adgj A (t) B (c) C (n) D (m)?
It is: D (m) because 2 letters of the alphabet are skipped over each time
What is the formula for the area of a triangular prism?
If the sides of the triangle are a, b and c and the length is d, then, area of triangular cross section t = sqrt[s*(s-a)*(s-b)*(s-c)] square units where s = (a+b+c)/2 and then total area = 2*t + (a+b+c)*d suare units = 2t + 2sd square units.
What are some five letter words with 1st letter C and 3rd letter T and 5th letter D?
According to SOWPODS (the combination of Scrabble dictionaries used around the world) there are 2 words with the pattern C-T-D. That is, five letter words with 1st letter C and 3rd letter T and 5th letter D. In alphabetical order, they are: cited coted
What are some seven letter words with 1st letter D and 5th letter C and 7th letter T?
According to SOWPODS (the combination of Scrabble dictionaries used around the world) there are 2 words with the pattern D---C-T. That is, seven letter words with 1st letter D and 5th letter C and 7th letter T. In alphabetical order, they are: deficit dovecot
