Simplify the expression（1+cotx）（1-cotx）-csc square x
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Simplify the expression（1+cotx）（1-cotx）-csc square x as far as possible.
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- The functions ¢1(x) and ø2(x) are normalized: d φ( (α) φι(α) dx 0(x) 62(x) = 1 = 1 -00 -00 and are mutually orthogonal dx oi(x) $2(x) dx 4i(x) $1(x) = 0 . Is the function b_(x) = ¢1(x) – $2(x) normalized? If not, determine its normalization constant and write the formula for the normalized y_ (x). Is the function +(x) = ¢1(x) + ¢2(x) %3D orthogonal to _(x)?Determine the indices for the direction shown in the following cubic unit cell: X Answer: Z For negative indexes use in front of the number. Use the proper type of brackets and no spaces. Answer: NIL Determine the Miller indices for the plane shown in the following unit cell: NIH y WIT For negative indexes use in front of the number. Use the proper type of brackets and no spaces.Question 2: Complete the following Error Analysis The lengths of the sides of a rectangular box are measured using a ruler marked with a millimeter scale. W The measurements give the values length 83 mm, width 68 mm and height 23 mm. The uncertainty in each measurement is ±1 mm. Calculate, 1. The fractional uncertainty in the measurement of VOLUME is 2. Absolute uncertainty in the measurement of VOLUME in (mm³ ) is
- Find the area of the region between the graphs of f(x) = 7x + 8 and g(x) = x + 2x +2 over [0, 2]. %3D (Use symbolic notation and fractions where needed.) A =solve 2c using engineering notationFind the gradient of the following functionsa) F(x,y,z)= x2 + y3 + z4b) F(x,y,z)= ex sin y ln zThe height of certain hill (in feet) is given by: h (x,y) = 10 (2xy-3x2-4y2-18x+28y+12) Where y is the distance in north, x is the distance in east.a) Where is the top of the hill located?b) How high is the hill?c) How steep is the slope (in feet per mile) at a point 1-mile north and 1- mile east, in whatdirection is the slope steepest?