Use a half-angle formula to find the exact value of tan 112.5°. tan 112.5° = √2 21 2 16 X 5

Q: 9. Which derivative does the limit lim h→0 (2+h)²2-4 Ih (A) f'(2) where f(x) = x² (B) f'(2) where…

A:

Q: b) The rectangles in the graph below illustrate a right endpoint Riemann sum for f(x) = 4 sin x on…

A: We have to find the value of the given reimann sum.

Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: , n=5a=0, b=4

Q: 2. table. Speedometer readings for a motorcycle at 12-second intervals are given in the t (second) 0…

A: (a) To estimate the distance traveled by motorcycle during this time period using the velocities at…

Q: When an object is removed from a furnace and placed in an environment with a constant temperature of…

A: The Newton's cooling law Temperature of the objectProportionality constant Enviornment temperature

Q: Your velocity is v(t) = ln(t² + 1) ft/sec for t in seconds, 0 ≤ t ≤ 2. Find the distance traveled…

A: Velocity is v(t)=ln⁡(t2+1)ft/sec for t in seconds, 0≤t≤2.

Q: Verify that the hypotheses of Rolle's Theorem are satisfied for f(x) = x² - 8x + 12 on the interval…

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Q: 1 Evalvate the following integrals (use method of integration by parts): 2 (₁) S (sinth) ² dre

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Q: he approximation ex = 1+x+ - is used when x is small. Use the Remainder Estimation Theorem to…

A: Given approximation ex =1+x+(x2/2).We have to find error in this approximation by using remainder…

Q: Find the local maximum of f(x,y) = xy(1-x-y) Find the critical point(s) and check the value of D = f…

A: given function

Q: Solve the following integration :- 3 S sin³x Sin³x cośx dx

A: The given integration is

Q: Write and solve the differential equation that models the following verbal statement. Evaluate the…

A: We solve the given problem by using the variable-separable method.

Q: 1 S² F(x) '9 +6² f(x) dx = 37 and g(x) dx= 18, find I' [3f(x) + 5g(x)] dx.

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Q: f(x) 3, 4x + A, Bx - 6, 10x + C, Dx + 6, 2, x 2

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Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied for f (x) = √√x + 4 on the…

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Q: Use the Chain Rule to check that the derivative of d dx 5 2(4-x-)- = = 1 (ਜ) 5 d 2 dx 5 2(4 – x²)² d…

A: We have to find the derivative of the given function using chain rule.

Q: If the marginal revenue for ski gloves is R'(x): = -0.7x + 40 and R(0) = 0, find the revenue…

A:

Q: Compute JJJ³ 32² dV, where W is the solid sphere x² + y²+z² ≤4.

A: Computewhere  is the solid shpere

Q: Let f(x) = x^4 − 4x^3 − 20  (a) Find the first derivative f'(x) and the second derivative f"(x)…

A: According to our guidelines we are supposed to answer only the first three subparts of the question.…

Q: Find horizontal asymptotes A) y = f(x)= x+3x-5 2x² + 3x³

A: Since you have asked multiple questions, as per company guidelines we will be answering only first…

Q: Use the taylor expansion up to the third iteration to approximate f(3) for the function f(x) =…

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Q: Use the transformation u = 3x + 4y, v=x+4y to evaluate the given integral for the region R bounded…

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Q: Consider the series. 8n (n+1)4²n+1 In this problem you must attempt to use the Ratio Test to decide…

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Q: Consider the following. y 16 8 0 y = f(x) 8 O R6 16 (a) Use six rectangles to find estimates of each…

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Q: tan ¹ (sin x) √√x D) lim-

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Q: Show that the curve r= sin(0) tan() (called a cissoid of Diocles) has the line x = 1 as a vertical…

A:

Q: f(x) = 3x - 2 Submit multiple values as a comma-separated list. Do not round any value. C=

A: Given function F(x) = x2/(3x-2) on (1,2)

Q: Solve the following integration :- پیمرا Sin 2 x dx - Cos³x 2

A: The given integral is sin2x/(1-cos2x)

Q: The rate at which a machine operator's efficiency, E (expressed as a percentage), changes with…

A:

Q: . The derivative, f', of a function f is plotted below. At approximately what value of x does f…

A: The derivative, f′, of a function f is plotted below. At approximately what value of x does f reach…

Q: Evaluate the following integral. Š 12x - 61 dx

A:

Q: 2. Determine the value of the discriminant for the quadratic equation y = 1.4x² - 6x +5 and use that…

A: we are given the quadratic equation and we need to find its discriminant.

Q: cos(x) dx 2) Calculate the integral sinc √sin(x)

A: To calculate the following integral.

Q: Sketch the region R bounded by the curves y = e, y = 1, and x = 2, and find the coordinates of the…

A: We have to find the coordinates of the centroid.

Q: for f(x) Verify that the hypotheses of the Mean-Value Theorem are satisfied √49 – x² on the interval…

A: we have given that

Q: * Lind the general Solution of - dy dr K X = xe

A: dy/dx = xex

Q: Tutorial Exercise If fis integrable on [a, b], the following equation is correct. [" f(x) dr = limf…

A: We have to find the value of the limit to evaluate the integral.

Q: Find the intervals of increasing and decreasing  for y= (sinx)/(2+cosx)

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Q: 5 Find f such that f'(x) = - √x f(16) = 49.

A: f′(x)=5x,f(16)=49

Q: Find the local maximum and local minimum values of f using both the First and Secon f(x) = 2 + 6x² -…

A: Given that f(x) =2+6x^2 - 4x^3We have to find local maxima and minima

Q: Cleany mulcate your strategy. 1. The vertical axis represents the height and the horizontal axis the…

A:

Q: 4. In this question we will consider the transformation given by the formulas and y = u-v. (a) What…

A: Changing of the independent variable.

Q: Evaluate the integral by interpreting it in terms of areas. L² (3x-14) de Part 1 of 3 We are…

A: To evaluate the following integral by interpreting in terms of areas.

Q: Find the general Solution For D-E dy = xỷ - cosx sinx dx y (1-x²)

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Q: Given u(x, t) = 3e, compute: 4, Uxx =

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Q: Find the general Solution For D-E cosy dx + (x Siny - 1) dy =o

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Q: Tutorial Exercise Evaluate the integral by interpreting it in terms of areas. f (x-14) de Part 1 of…

A:

Q: Given the values of the derivative f '(x) in the table and that f(0) = 195, estimate the values…

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Q: 7. Find lim to talk A. 1 C. -1 B. 0 D. does not exist

A: We have to evaluate the limit.

Q: * Find the general Solution of :- - dy хе dxx New 1=Y, NOVIR VO

A: The given equation is; dy/dx = xex