1. Let f(x) = x on the interval [-r, T]. (a) Compute |f|12, given by dæ\1/2 \f(x)2 27T (b) Compute f(0), given by - f(0)=_ da f (x) 2 -T

Q: 1- f(x,y) = In(x² + y?) at (1,1)

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: 1. If f(x) cos(t) dt, then f'(x) =

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Q: 4. (5pt) If f(r) = [t – 1) cosh t dt, on what interval is ƒ increasing? (Hint: Use the Fundamental…

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Q: Is there a sequence of continuously differentiable functions: fn : R –→ R such that fn → x and f. →0…

A: Yes, the sequence is given in step 2.

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

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Q: Find the linearization of f(x) = (1+ x)20 at x = 0. Use it to approximate (1.001)20.

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Q: If f(x)= integral subscript 2 superscript x fraction 1+t/1+t^2 dt, then what is f'(-3)?

A: f(x)=∫2x1+t1+t2dt, find f'(-3)

Q: Prove that = va² – x* if y =(f)sin~+ () + (9)v&* - x²

A: Differentiation wrt x

Q: 1. Let the function f: R R be given by 1- cos(x) if x + 0, f(x) := if x = 0. 1 Prove that f is…

A: Differentiablity analysis problem....

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

A: Please see the answer below

Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits…

Q: 2. Let f(x, y) = In(x² + y²). Show that fre + fyy = 0. %3D

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Q: 4. Integrate the function f(z) = z² + 2z from z = -i to z = 1 in two ways, once along a straight…

A: The objective is to integrate the function fz=z¯2+2z from z=-i to z=1 in two ways, Once along the…

Q: 2. Let f(x) = S dt for x 2 2 In a) Find F'(x). b) Is F increasing or decreasing? What can you say…

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Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz əz (B)If Z…

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Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

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Q: (-x + 1for x 1 h(x) h is continuous at x=1

A: A function is continuous at a point x=a if it satisfies all the three conditions. 1) Function must…

Q: 1 - t Let F(x) = dt for -o << x < +∞ t2 + 24

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Q: (3) If the functions f(x) and g(x) are continuous 0sxS1, then f(x)/ g(x) is continuous on the…

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Q: 3. Consider f : R2 → R defined by f(x,y) = y³ + 3x²y – 6x² – 6y? + 2. - (a) Determine the critical…

A: The given function is: f(x,y)=y3+3x2y-6x2-6y2+2

Q: 7. Suppose that f: R R is differentiable at c and that f(c) = 0. Show that g(x):= |f(x)| is…

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Q: 4. Find the maximum value of f (x) = In(x – In x) on the interval -sse. e

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Q: Use a linear approximation to estimate f(0,1), given that y=f(X) is a differentiable  with f(0)=1…

A: Consider the given information

Q: 4. Find the first two intervals using the bisection method to compute the minimum of the function…

A: We need to find the first two intervals of on the interval

Q: 19.D. Show that the function defined by g(x) g² sin (1/x), x * 0, %3D = 0, 0, is differentiable for…

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Q: Find an equation of the line tangent to f(x) = xcos x at x = -4. (Round coefficients to 3 decimal…

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Q: 9. Suppose f(x) is continuous and f(x)dx = 10, f(x)dx the equation f(x) = 1 has a solution on the…

A: Divide the interval [-5,5] in to two sub intervals [-5,-1] and [-1,5]

Q: Assume that f'(c) = 0 and that f'(x) changes from + to - at the critical point x = c. This means…

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Q: If f is differentiable everywhere and f(1)=f(2)=π, then ∫12 f'(t)dt=0   True or false?

A: True because,

Q: 2.4 Use the definition of the derivative of complex function to show that f(z) is not dif-…

A: The Complex Derivative Definition: Let f be a function defined on a neighborhood of z0 ∈ ℂ. If…

Q: 3. Show that x? if x>0 0 if x<0 f(x) = is differentiable at xo =0 but f' is not differentiable at xo…

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Q: 1. Show that function f(x)=D|x | is not differentiable at 0

A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

Q: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

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Q: 20. The function f is continuous at x = 1. Vx + 3 -. - V3x + 1 for x 1 x - 1 If f(x) = k for x = 1…

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Q: b) Show that the function f (x) = { * x² sin ! for x E (0, 1] for x = 0 is absolutely continuous on…

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Q: Σ sin k+1

A: to show that the given series ∑k=1∞1ksinxk+1 converges uniformly on R to a differentiable function f…

Q: Suppose that f is a differentiable function with f(2) = 5 and f'(2) = 7. Let h(x) = f(e*). Find an…

A: Find the derivative for the function h(x). Now, the derivative for the function is the slope for the…

Q: 5.) Use linear approximation to estimate f(0.1, −0.9) x² sin x In(y² + 1) Y f(x, y) = of th + x+1…

A: NOTE: Refresh your page if you can't see any equations. . here we want to find the approximate…

Q: 3 - x, x<2 Q.No.15: Is f(x) = {+2 x22 continuous at every x € R. x+1 xs1 -.

A: Continuity of a function.

Q: If ƒf (x) =¸ (A) (B) Sº sec²x 1+elanx In (secx) √✓ 1+tan²x tanx 1+e sec ³x tanx 1+e 1+1² tanx…

A: Using Leibnitz integral rule.

Q: 7. Find the c value(s) that satisfy Rolle's Theorem for the function f (x) = x* – 4x² on the…

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Q: 1. Show that the function x2 – y2 2xy f(x,y) ={ x2 + y? if (x,y) # 0 if (x, y) = 0 is continuous at…

A: If for every ε&gt;0, there exists a δ&gt;0, such that if |x-a|&lt;δ, |y-a|&lt;δ, then the function…

Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

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Q: if f(x)=integral t^3+5t^2+6, from 0 to x. what is f''(x)=?

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Q: 3. Let f)=x+x+2x-1E2,lx). Then x= 1 is a root for r() of mmltiplicity 3D1 None 4 2

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Q: 13. Prove that the function 2x 1 dt t F(x) is a constant on the interval (0, ∞ )

A: The student has specifically asked for the solution to Question-13. Hence, that question is solved…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.