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(1) Use the Squeeze Theorem to show that limx-ox* cos(207x) = 0. Give all your reasons....
Use the ε - δ definition for the limit to prove that limx→-2 (4x - 3) = -11
2. Use the ε - δ definition for the limit to prove that limx→-2 (4x - 3) = -113. Use the limit definition of the derivative to find the derivative of the function f(x) = √(4x + 1)4. Find the equation of the tangent line to the curve ve y = (1 + 2x) 10 at the point (-1,1).
#23 22, Use the definition of limit to prove Theorem 3.5. 23. Use Theorem 3.5 to...
#23
22, Use the definition of limit to prove Theorem 3.5. 23. Use Theorem 3.5 to prove that lim x? cost(1/x)-0. In addition, give a proof of th result without using Theorem 3.5. THEOREM 3.5 Squeeze Theorem for Functions Let I be an open interval that contains the point c and suppose that f, g, except possibly at the point c. Suppose that g(x) s f(a) s h(x) for all x in I If limn g(x)-L = lim h (x),...
1. If a particle moves according to a law of motion S(t)=12-6-7, t 20 Where t...
1. If a particle moves according to a law of motion S(t)=12-6-7, t 20 Where t is measured in seconds and sin meters, (a) Find the velocity of the particle in terms of t. (b) Find the velocity and the speed at time t=1. (c) When is the particle at rest? (d) When is the particle moving to the right and when is it moving to the left? (e) Find the acceleration of the particle at t. (10pts) 2. Evaluate...
Section 2.6 Homework (continued) D. Determine the end behavior of the following function. (Do this algebraically.)...
Section 2.6 Homework (continued) D. Determine the end behavior of the following function. (Do this algebraically.) $ 16x8 – 12x2 f(x) = 1- 7x² + 5x 70 + 2X-8 C. Find the limit or show that it does not exist. (a.) lim n sin²x " (Hint: Use squeeze theorem) X x²+1 (b.) lim cot?(-Inx) (Do this analytically.) X-> Section 2.6 Homework (continued) E. Find the following limits if they exist. Explain. (Do this analytically (a.) lim cot' (In 10 -...
(complete the proof. Hint: Use the Squeeze Theorem to show that lima = L.) 3- For...
(complete the proof. Hint: Use the Squeeze Theorem to show that lima = L.) 3- For all ne N, let an = Let S = {a, neN). 3-1) Use the fact that lim 0 and the result of Exercise 1 to show that OES'. 3-2) Use the result of Exercise 2 to show that S - {0}. 4- Prove that
Calculus 1 MAT 201 Final Exam, Spring 1 2019, LAGCC Evaluate the following limits, you may...
Calculus 1 MAT 201 Final Exam, Spring 1 2019, LAGCC Evaluate the following limits, you may use L'Hospital's rule, if it applies. -V31+4 lim 4-1 -4 a. b. Evaluate the following limit. lim xIn x x-0 2. Evaluate and explain your answer -xsin(x)+cos (x) x+1 130 dx (a.) 130 Differentiate each of the following below using the fundamental theorem of calc part 1 X cos? (1- 51) dt ) g (x) = S_ e (2c) g(t)= J x2t+1 3 Use...
1-Given the function:
1-Given the function: \(y=\frac{x^{2}-3 x-4}{x^{2}-5 x+4}\), decide if \(f(x)=y\) is continuous or has a removable discontinuity, and find horizontal tond vertical asymptotes.2 A-Use the definition \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\) to prove that derivative of \(f(x)=\sqrt{4-x}\) is \(\frac{-1}{2 \sqrt{4-x}}\)2 B- Evaluate the limit \(\lim _{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}\) for the given value of \(x\) and function \(f(x) .\)$$ f(x)=\sin x, \quad x=\frac{\pi}{4} $$3-Given the function: \(y=(x+4)^{3}(x-2)^{2}\), find y' and classify critical numbers very carefully using first derivative tess...
Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'()...
Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'() -- 3cos(3x) sin(sin(3x)) Of'(x) - 3cos(3x) sin(cos(3x]) f'x) --sin(3x) cos(cos(3x)) Question 2 1 pts Find the derivative of f(x) = cos(x^2 + 2x). Of "(x)=2x+2 sin(x^2 + 2x) O f'(x)= x^2 sin(x^2+2x) Of"(x)= (2x+ 2) sin(x^2 + 2x) f'(x)= -(x^2 + 2) sin(x^2 + 2x) O f'(x)--(2x + 2) sin(x^2 + 2x) Question 3 1 pts Use implicit differentiation to find the slope of...
Referring to the graphs given below, use properties of limits to find each limit.
Referring to the graphs given below, use properties of limits to find each limit. If a limit does not exist then state that it does not exist. y = f(x) y = g(x) lim f(x)= lim g(x) = f(x) x- lim x+0 g(x) lim lim g(x) = lim [f(x)+g(x)] = x-1 lim f(x) = lim g(x) = lim --+ f(x) h- h derivative of f(x) = 2x² + 3x is f'(x) = 4x +3. The steps are what count here!...
solve d-f Find the limits and show your work. Use L'Hospital's Rule where appropriate. (a) lim-0...
solve d-f
Find the limits and show your work. Use L'Hospital's Rule where appropriate. (a) lim-0 tan 3.0 2.2 1 (b) limu+0+ In(X) (c) limx→ In(x + 3) – In(3x + 2) (d) limz+ x sin(5) (e) lim.+ 22-45 4" +3: (f) limo (#2) (g) lim + (e+ + a)*
#23
22, Use the definition of limit to prove Theorem 3.5. 23. Use Theorem 3.5 to prove that lim x? cost(1/x)-0. In addition, give a proof of th result without using Theorem 3.5. THEOREM 3.5 Squeeze Theorem for Functions Let I be an open interval that contains the point c and suppose that f, g, except possibly at the point c. Suppose that g(x) s f(a) s h(x) for all x in I If limn g(x)-L = lim h (x),...
1. If a particle moves according to a law of motion S(t)=12-6-7, t 20 Where t is measured in seconds and sin meters, (a) Find the velocity of the particle in terms of t. (b) Find the velocity and the speed at time t=1. (c) When is the particle at rest? (d) When is the particle moving to the right and when is it moving to the left? (e) Find the acceleration of the particle at t. (10pts) 2. Evaluate...
Section 2.6 Homework (continued) D. Determine the end behavior of the following function. (Do this algebraically.) $ 16x8 – 12x2 f(x) = 1- 7x² + 5x 70 + 2X-8 C. Find the limit or show that it does not exist. (a.) lim n sin²x " (Hint: Use squeeze theorem) X x²+1 (b.) lim cot?(-Inx) (Do this analytically.) X-> Section 2.6 Homework (continued) E. Find the following limits if they exist. Explain. (Do this analytically (a.) lim cot' (In 10 -...
(complete the proof. Hint: Use the Squeeze Theorem to show that lima = L.) 3- For all ne N, let an = Let S = {a, neN). 3-1) Use the fact that lim 0 and the result of Exercise 1 to show that OES'. 3-2) Use the result of Exercise 2 to show that S - {0}. 4- Prove that
Calculus 1 MAT 201 Final Exam, Spring 1 2019, LAGCC Evaluate the following limits, you may use L'Hospital's rule, if it applies. -V31+4 lim 4-1 -4 a. b. Evaluate the following limit. lim xIn x x-0 2. Evaluate and explain your answer -xsin(x)+cos (x) x+1 130 dx (a.) 130 Differentiate each of the following below using the fundamental theorem of calc part 1 X cos? (1- 51) dt ) g (x) = S_ e (2c) g(t)= J x2t+1 3 Use...
Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'() -- 3cos(3x) sin(sin(3x)) Of'(x) - 3cos(3x) sin(cos(3x]) f'x) --sin(3x) cos(cos(3x)) Question 2 1 pts Find the derivative of f(x) = cos(x^2 + 2x). Of "(x)=2x+2 sin(x^2 + 2x) O f'(x)= x^2 sin(x^2+2x) Of"(x)= (2x+ 2) sin(x^2 + 2x) f'(x)= -(x^2 + 2) sin(x^2 + 2x) O f'(x)--(2x + 2) sin(x^2 + 2x) Question 3 1 pts Use implicit differentiation to find the slope of...
solve d-f
Find the limits and show your work. Use L'Hospital's Rule where appropriate. (a) lim-0 tan 3.0 2.2 1 (b) limu+0+ In(X) (c) limx→ In(x + 3) – In(3x + 2) (d) limz+ x sin(5) (e) lim.+ 22-45 4" +3: (f) limo (#2) (g) lim + (e+ + a)*
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