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Q-2: a) Find the limts of: 1: lim (x cotx) sin 7x 2: lim 4x x²+x-2 3: lim x-x (9 marks) b) Find the derivative of the functions: 1- y= In tanh 2x 2- y = cseh (x+1) (6marks)
find the limits analytically, show all steps x²–8 1. lim *+2 X-2 2. lim x3 Vx+1-2 x-3 1 3. lim 3+ x 3 x2 - 2x -15 4. lim *+-3 x2 + 4x +3 x0 X (4+ x)-16 5. lim X>0 x² - 4 6. lim 1+2 r -8 x x+sin x 7. lim 10 X sin²x 8. lim :-) x 3 sin(4x) 9. lim *** sin(3x) r? 10. lim 1981-COSI 1 11. lim x → X-1 = 1 12....
can someone help? 1 +-+ - - ---- ---- -L1-L-IL 1-T + ---- + - 1 11 --+--- 1 TO LILI 11111 -15 f(x) = x2 - 9x - 10 x2 - 4x - 32 1. lim f(x) = *8 2. lim f(x) = 3. lim f(x) = x-+-4 4. lim f(x) = -4+ Note: You can earn partial credit on this problem.
Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. lim x?cotx X0 lim x?cotx = x+0 (Type an exact answer.)
If 4x s g(x) = 2x4 – 2x2 + 4 for all x, evaluate lim g(x). x →1
FInd u(x,t) and lim u(x,t) Solve the heat problem Ut = Uzx + 5 sin(4x) - sin(2x), 0 < x <7, u(0,1) = 0, u(,t) = 0 u(x,0) = 0
-4x+1 1) (15 pts) Evaluate lim X-V1672+5
7. Evaluate each of the following limits. tan x e-4x -e 4x a) lim x0 2x b) lim XOCOS X+1
Find the limit lim (V2x2 + 4x +1 – V2x2 + x - 1). Show 300 your work in the PDF version of the test.
Solve the following partial differential equations using the Laplace transform method. x〉o, 2 5 ,>0 lim u(x, ,) = 0, u(0,,)-1, 3) İhu Ot x〉o, 2 5 ,>0 lim u(x, ,) = 0, u(0,,)-1, 3) İhu Ot