Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 9 lim t-0 1 + t ty

Q: Use the rules of differentiation to find the derivative of the fur f(t) = -2t2 - 4t - 5 f '(t) =

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Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8  

Q: jpechudu - 2tan"e.c tan "(sinhu) - c

A: To prove:- ∫ sechu du =2 tan-1(ex) +C                     = tan-1(sinhu) +C 

Q: Find the general solution of the following homogenous lineare 1. (D² +5D + 6)y = 0 %3D 2. (2D? – 5D ...

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Q: (a) Evaluate sin 2z -dz, 3z -ĝi where C is an anticlockwise unit circle centred at the origin.

A: Follow the procedure given below.

Q: Determine the order of the differential equation. y' + y = 7y2

A: We have to Determine the order of the differential equation.

Q: he monthly cost of driving a car depends on the number of miles driven. Lynn found that in May her d...

A: Given query is to find the linear relationship , slope and the graph.

Q: Find the derivative of x/ex^2.

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Q: 2. Suppose that h(x) is a continuous function, h(-1/4) = 1/2, h(7/4) = 1 and h(2)dx = 2. Evaluate th...

A: Here, given that h-π4=12, hπ4=1 & ∫-11h(x)dx=2...(1)

Q: Find the indefinite integra

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Q: A ship carrying 1000 passengers is wrecked on a small island from which the passengers are never res...

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Q: Evaluate the indefinite integral. 4 In(5 – x) dx

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Q: 4 z = lim f(x) y 1 2 3 4 2.

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Q: 30 25 (11,20) 20 15 10 -5 -10 -15 -20 (19, -15) -25 -30 20 -15 -10 -5 5 10 15 20

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Q: Sx (x +1) /3 dx

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Q: Find the limit. est – 1 lim t-0 sin(t)

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Q: 7- 3t+ sin 6t Find the limit of f(t) = as t approaches - 6t + cos 6t 1 lim f(t) = 2 t→- 00

A: Given problem:-

Q: What is the average rate of change of f(x) from x1 = -0.2 to x2 = 7.8? Please write your answer roun...

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Q: Use a tree diagram to write out the Chain Rule for u = f(x, y), where x = x(r, s, t), y = y(r, s, t)...

A: Given u=f(x,y) where x=x(r,s,t) and y=y(r,s,t) 

Q: 1. A piece of wire 36in. is cut into two parts, one of which is bent into the shape of an equilatera...

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Q: sechudu - 2tan".c -tan (sinhu) - C

A: Use the exponential form of sechu and easily prove the integral.I have used many inverse trigonometr...

Q: We want to estimate f(1.01 , 0.97) for the function f(x,y)= √(4 - x2 - y2). For this, we can use an ...

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Q: Do not skip any steps Find the numerical value of both expressions. Give the exact value and do not ...

A: QUESTION-  Find the numerical value of both expressions. Give the exact value and do not use a calcu...

Q: Use Midpoint approximation with n = 6 equal subintervals to approximate the following. 1 ln(x + 16...

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Q: 1 – 2xy)y' = yly + sinx] ; when x = 0, у %3D 1 + cosx 1+y²

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Q: Find the exact length of the curve.   y= 2/3x3⁄2,    0 ≤ x ≤ 4

A: Given query is to find the length of the curve for the interval.

Q: Solve the following inequalities by the verification method and indicate the solution set on the rea...

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Q: The table gives the output values that a function assigns to given input values. Input (x) Output ...

A: Given table Input (x) Output (y) −2 −8 4 10 9 25 12 34

Q: - - 3. (D2 – 3D + 2)y = 2x³ – 9x2 + 6x

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Q: If the limit of f(x) is 5 and the limit of g(x) is 2 as × approaches a constant k, what is the limit...

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Q: 8) Solve the initial value problem. y'(x) = y(4x' +1), y(0) = 4

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Q: y = sin(Ax + B)

A: Given: y=sin(Ax+B)

Q: Find the complementary angle of 45.2°. The complementary angle of 45.2° is °. (Type an integer or a ...

A: Complementary agle =90°-angle  =90°-45.2° =44.8°

Q: Use the graph of f (x) = – below to find a number & such that f (x) – 0.25| < 0.1 whenever 0< |x – 4...

A: Here, f(x)=1x is the given function.

Q: The position, in metres, of a particle moving in a straight line is given by the equation 30 s(x) + ...

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Q: Evaluate using trigonometric substitution ∫1/(x^2√1+4x^2)dx

A: Given that: ∫dxx21+4x2

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consi...

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Q: dx (2² + 4)3/2

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Q: Let f(x, y)= Jxy +x+xcos y. (a) Find fy - ở² f_ (b) Find дхду

A: f(x,y)=xy+x+x cos y

Q: What is the instantaneous rate of change for α=arctan(2-r/r) at r=0

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Q: ) Differentiate:  (a) f(x) = √x(cos)x2 (b) f(x) = 2x/x2 + 4

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Q: estimate the following limits and the function value. Complete parts (A) through (D). Use the graph ...

A: This question is related to limit. Solve in step 2.

Q: Jse the Quotient Rule to find the derivative of the function. cos(t) f(t) (t)

A: We will use the quotient rule of differentiation to find the derivative.

Q: Find 4 of 3xy –- x³ = 5 at (1, 2)

A: Given; 3xy-x3=5 at (1,2)

Q: Write the following in terms of sine, using the cofunction relationship. cos(5π/9)

A: We have to write in sin form.

Q: Evaluate using trigonometric substitution ∫(x+4)/(x^2-9)dx

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Q: use implicit differentiation to find

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Q: Scsc' xcot' x dx S(x + sin x) dx S sec' x dx

A: We have to find the indefinite integral.

Q: The table below shows some ordered pairs for an exponential function ff. x 0 1 2 3 f(x) 51.2 6.4 0....

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Q: Southern Traditions sold the home decor division of their company 8 years ago and immediately invest...

A: Topic =Algebra