Problem 5: Evaluate log(x) Jo 4+2 0 3. Show that 2x cos(e) Jo 1-cos(0) Problem 5: Evaluate log(x) Jo 4+2 0 3. Show that 2x cos(e) Jo 1-cos(0)
Evaluate (T/4 sinº (2x) cos (2x) dx. 17/12 Round your answer to 2 decimal places if necessary. For what value of kis the area under the graph of y = 3x2 + 4kx between x = 0 and x = 1, equal to 3? Round your answer to 2 decimal places if necessary. Evaluate 1 x (x + 2x + 1) dx. Jo Evaluate cos (T) da. Cvaluate 5 (23 + 4) dx.
Exponential and logarithms 2 log 5 + 1/2 log x = 2 4 : 0.2 e 2x-4 - 10 slog 2 (3x+1) + log 2 (2x - 1) = 3
solve each equation algebraically: a) 3+7e^2x=24 b) 2^x+5=7^3x+1 c) 3^(2x) - 3^(x) - 20=0 d) log x + log (x-5)=2 ^6 ^6 e) log(x+2)-log(x-1)=1 f) ln(log (x^2 + 2x))=0 ^3 d og, 71 Solve each of the exponenti a tions call the as well as a decimal approximation to the nearest the get the approximated solutions Yo d ac t o a) 3+72-24 d) 3 -3-20 - 0 get the approximated solution a) loe +log.-5) = 2
1P Question 3 1 Evaluate the double integral: SS sin?(x) dx2 7 o (+ cos(2x)) 0} (x2 + cosº (x)) No answer text provided. 0}(– cos(2x)) 0} (x + 2 cos(2x)) NE Previous
A)Find the inverse of the function f(x)=3+{2x-1 B) SOLVE log(x+2)+log 3 (x-2)=2 5. 6. vords e here to search ORI
Question 5 (20 marks) a) [10 marks] Evaluate: 1 el-X Vx+y(y – 2x)2 dydx. 0 Jo (Hint: consider a change of variable.) b) [10 marks) Find the volume of the solid bounded by the sphere x2 + y2 + z2 = aand the cylinder x2 + y2 = ax, a > 0.
Problem 6 Evaluate: dx 16 - 22 Hints: sin²x = 1 - cos(2.0) and sin(2x) = 2 sin c cos r. 2 (Show all details.)
Evaluate a) integral 0 to pi (dx/5-4 cos x) b) integral 0 to infinity (dx/(1+x^2)^3)
2x 1 Use a contour to evaluate dᎾ (2+0 -cos)