theorem 7

Use the fundamental theorem of calculus to evaluate ∫ -3 0 x x 2 + 5 dx . => - 1 2 ln ( 5 1 4 ) or ln ( 5 1 4 ) or 1 2 ln (14) or - 1 2 ln (7) or 1 2 ln ( 5 1 4 )..

Use the rational zero theorem to list all the possible rational zeros for f ( x ) = x 4 + 5 x 3 - x 2 - 4. =>± 1; ± 2; ± 4 or ± 1; ± 2; ± 5; ± 10 or ± 1; ± 2; ± 3 or ± 1; ± 7..

Find the value in the interval, which satisfies the Mean Value Theorem for the function f ( x ) = x + 2 2 x on [ 1 2 , 2]. => 7 3 or 5 2 or 1 or 0 or - 1..

Any point (or every point) on the perpendicular bisector of the line segment joining two given points is equidistant from them..

Question: Solve the following equation: Answer: 2x-(1-2x) = 5-3(1+x) 2x-1+2x = 5-3-3x 4x+3x = 5-3+1 7x=3 ..

Question: Find the equation of the line perpendicular to the line 8x + 5y = 7 and passing through (1, 2). Answer: ( Product of slopes of two perpendicular lines = -1) ..

But the displacement when the bus moves from A B and then from B A is zero. SI unit of displacement is metre. Displacement is a vector, i.e., the displacement is given by a number with proper units and direction. To drive home the difference between displacement and distance let us consider a few m..

Molecule Example Degrees of Freedom Predicted Molar Specific heats Translational Rotational Total (f) Cv Cp = Cv + R Monatomic He 3 0 3 3/2 R 5/2 R Diatomic O 2 3 2 5 5/2 R 7/2 R Polyatomic CH4 3 3 6 3 R 4 R The above table shows th..

>By binomial theorem, h is assumed to be very small when compared to radius R of the Ea..

. The side adjacent to q is the side AB. The hypotenuse of the D ABC is the side AC. Now, let us write down the trigonometrical ratios with the help of the above triangles: (i) Sine q : It is defined as the ratio of the side opposite to q and the hypotenuse. i.e., In short we write sin (ii) Cosine ..