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5. Jula found the derivative of some function and obtained the following: sinx f'(x) = 1+...
tion 5 sinx Use Part 1 of the Fundamental Theorem of Calculus to find the derivative...
tion 5 sinx Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function h(x) 3int dt h'(x) = 3 cos(x)In(sinx) - h'(x) = 3 in (cos(x)s in(x))+ 1m3) - h'(x)=3\n(sin(x)cos(x)) - 31nYX h'(x) - 3sin(x) 31n(7) cosx 2 n'(x) = () - 3cos(x) 3inx sinx x h"(x) = 3sin(x)in(cosx) + 3inky 2x
Question 17 Find the derivative of the function f(x) = 4e*cosx . Simplify your answer. 0...
Question 17 Find the derivative of the function f(x) = 4e*cosx . Simplify your answer. 0 a. 4e*(cosx-sinx) 0 b. 4e*(cosx + sinx) 0 C. 4e*cosx ( d. 4e*sinxcosx e. -4e* sinx A Moving to another question will save this response.
og sinx cost D Check if the integral Sinx cosx dx is aboulte convergent, conditionally convergent...
og sinx cost D Check if the integral Sinx cosx dx is aboulte convergent, conditionally convergent or divergent let f«) contiewos, positive, decreasing function (0,1] such that SEGAOX convergent. Prove: lim xfx=0 on Xtot 5 let f be integrable function on [1]. foss x H XE [o,(Excluding some points). Prove that $x + 6) dx = }} Tip is for integrable, so is xf(x)
Let 17x2 + sinx -- 6. 1+r2 T And let h be a function of the...
Let 17x2 + sinx -- 6. 1+r2 T And let h be a function of the derivative 8(x) = efv1 + x2 1+ arctan2x A) Let f1(x) = h(x)cosx. what is f'1(0)? B) Let f2(x) = g(6x+h(x)). what is f '2 (0)?
Is x = 0 a relative extrema for function f : R → R that is...
Is x = 0 a relative extrema for function f : R → R that is given
by f(x) = sinx − cosx − 1/2(1 + x)^2
Question 3. Is x = 0 a relative extrema for function f:R + R that is given by 1 COS X f(x) = sin x (1 + x)? 2 Prove your claim. State any theorem that is applied in your proof.
Q1. If g(x)=4cosx, then a) 4sinx b) -4 sinx c) -4cosx d) 4cosx Q2. The derivative...
Q1. If g(x)=4cosx, then a) 4sinx b) -4 sinx c) -4cosx d) 4cosx Q2. The derivative of the function f(x)=-9x2 + 5x at x=-3 is a) -10 b) 41 c) 36 d) -49 x54 Q3. If g(x)= 3x +6x, *S*. then lim g(x)= =........ 8x+10, a) 48 b) 24 c) 72 d) 42 Q4. Find: lim (5+h)-25 Q5. Find: limano sin Q6. If y=x-*+cosx , then finden Q7. Using the definition, determine whether the function X57 is continuous at x=7....
Question 12 Find the derivative of the function f(x)= (in(cox) + sinº(x))2. • f'(x) = 12(In(cox)...
Question 12 Find the derivative of the function f(x)= (in(cox) + sinº(x))2. • f'(x) = 12(In(cox) + sin?(x)) (3sin?x cosx – tanx) • f'(x) = 12(In(cox) + sin?(x))+(3sinx cos?x - tanx) o f'(x) = 12(In(cox) + sin(x))(3sinx cosx + tanx) o f'(x) = 12(In(cox) + sin}(x))^2(3sin?x cosx + tanx) A Moving to another question will save this response.
sinx 5. (10 marks) Check whether f (x) = if x = 0 if x =...
sinx 5. (10 marks) Check whether f (x) = if x = 0 if x = 0 is differentiable at x-0. Prove it using an e- 8 proof. sinx 5. (10 marks) Check whether f (x) = if x = 0 if x = 0 is differentiable at x-0. Prove it using an e- 8 proof.
Verify that the indicated function is a solution of the given differential equation. dy 1 +y=sinx...
Verify that the indicated function is a solution of the given differential equation. dy 1 +y=sinx : y= 2 sinx dx Cosx +10e-X
4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c) 4. Find the following limits by using L'Hôpital's rule. 1 +...
4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c)
4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c)
tion 5 sinx Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function h(x) 3int dt h'(x) = 3 cos(x)In(sinx) - h'(x) = 3 in (cos(x)s in(x))+ 1m3) - h'(x)=3\n(sin(x)cos(x)) - 31nYX h'(x) - 3sin(x) 31n(7) cosx 2 n'(x) = () - 3cos(x) 3inx sinx x h"(x) = 3sin(x)in(cosx) + 3inky 2x
Question 17 Find the derivative of the function f(x) = 4e*cosx . Simplify your answer. 0 a. 4e*(cosx-sinx) 0 b. 4e*(cosx + sinx) 0 C. 4e*cosx ( d. 4e*sinxcosx e. -4e* sinx A Moving to another question will save this response.
og sinx cost D Check if the integral Sinx cosx dx is aboulte convergent, conditionally convergent or divergent let f«) contiewos, positive, decreasing function (0,1] such that SEGAOX convergent. Prove: lim xfx=0 on Xtot 5 let f be integrable function on [1]. foss x H XE [o,(Excluding some points). Prove that $x + 6) dx = }} Tip is for integrable, so is xf(x)
Let 17x2 + sinx -- 6. 1+r2 T And let h be a function of the derivative 8(x) = efv1 + x2 1+ arctan2x A) Let f1(x) = h(x)cosx. what is f'1(0)? B) Let f2(x) = g(6x+h(x)). what is f '2 (0)?
Is x = 0 a relative extrema for function f : R → R that is given
by f(x) = sinx − cosx − 1/2(1 + x)^2
Question 3. Is x = 0 a relative extrema for function f:R + R that is given by 1 COS X f(x) = sin x (1 + x)? 2 Prove your claim. State any theorem that is applied in your proof.
Q1. If g(x)=4cosx, then a) 4sinx b) -4 sinx c) -4cosx d) 4cosx Q2. The derivative of the function f(x)=-9x2 + 5x at x=-3 is a) -10 b) 41 c) 36 d) -49 x54 Q3. If g(x)= 3x +6x, *S*. then lim g(x)= =........ 8x+10, a) 48 b) 24 c) 72 d) 42 Q4. Find: lim (5+h)-25 Q5. Find: limano sin Q6. If y=x-*+cosx , then finden Q7. Using the definition, determine whether the function X57 is continuous at x=7....
Question 12 Find the derivative of the function f(x)= (in(cox) + sinº(x))2. • f'(x) = 12(In(cox) + sin?(x)) (3sin?x cosx – tanx) • f'(x) = 12(In(cox) + sin?(x))+(3sinx cos?x - tanx) o f'(x) = 12(In(cox) + sin(x))(3sinx cosx + tanx) o f'(x) = 12(In(cox) + sin}(x))^2(3sin?x cosx + tanx) A Moving to another question will save this response.
sinx 5. (10 marks) Check whether f (x) = if x = 0 if x = 0 is differentiable at x-0. Prove it using an e- 8 proof. sinx 5. (10 marks) Check whether f (x) = if x = 0 if x = 0 is differentiable at x-0. Prove it using an e- 8 proof.
Verify that the indicated function is a solution of the given differential equation. dy 1 +y=sinx : y= 2 sinx dx Cosx +10e-X
4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c)
4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c)
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