(In2)2 +1 -2 sin r+ (In 2)2 cos x Evaluate /2 cos z da In 2 2° cos x + 2° sin (In 2) ln 2 1 +ln2 ...
(1 point) Fill in the blanks: 1. If tan r 3.5 then tan(-z) - I 2. If sin a 0.7 then sin(=x) = 3. If cos r 0.2 then cos(-r)=| 4. If tan r 1.5 then tan(T+ x)=| (1 point) Fill in the blanks: 1. If tan r 3.5 then tan(-z) - I 2. If sin a 0.7 then sin(=x) = 3. If cos r 0.2 then cos(-r)=| 4. If tan r 1.5 then tan(T+ x)=|
Evaluate the integral using a change of variables. Z ZR (x + y) sin(x − y) dA (Z's are integrals) where R is the triangular region with vertices (−1, 1), (1, 1), and (0, 0).
Evaluate the double integral f(r, ) dA. 7/6 2 p2 sin(O) cos(O) dr do Jo Jo Enter a fraction, integer or exact decimal. Do not approximate.
4. Evaluate the definite integrals: A) |_ In xdx 1 xV1+ ln² x I dx cos x sin x a f / Inx di -d
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
6. Use l'Hopital's rule to evaluate the following limits 1+cos (Te sin(z) (a) lim z-+0 log (-1) (b) lim 92I-2 cos(TI) (c) lim r sin Page 2 of 2 0 words
Evaluate Sc (2+2)dy where C is described by parametric equations x(t) = cos(t), y= sin(t), z = 2,0 <t< Select one: O A. +2 O B. 1+2 O C.-1 OD. -1 ABC is a triangle in R where A =(1,4,5), B =(2,-1,0) and C =(4, 2, -3). Find the area of ABC. Select one: O A. (-30,7, -13) O B. -2 OC. V1118 O D. VILLE
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.
Find the derivatives of the following functions. a) f(x) = sin(x²) b) g(x) = ln(cos(x)) c) h(z) – In(1002? + 47x)? d) k(z) = resin(2)
Evaluate the integral by making an appropriate change of variables. Slo 3 cos (5(X+3) dA where R is the trapezoidal region with vertices (8,0), (9, 0), (0, 9), and (0,8) 17 sin(5) 2 x