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(Solved): Do the following with the given information. \int_0^1 27cos(x^(2))dx (a) Find the approximations T_( ...



Do the following with the given information.

\int_0^1 27cos(x^(2))dx

(a) Find the approximations

T_(8)

and

M_(8)

for the given integral. (Round your answer to six decimal places.)

T_(8)=,✓ Great work. M_(8)=,✓ Great jobt

(b) Estimate the errors in the approximations

T_(8)

and

M_(8)

in part (a). (Use the fact that the range of the sine and cosine functions is bounded by

!=1

to estimate the maximum error. Round your answer to seven decimal places.)

|E_(T)|<= |E_(M)|<=

q,

q,

(c) How large do we have to choose

n

so that the approximations

T_(n)

and

M_(n)

to the integral are accurate to within 0.0001 ? (Use the fact that the range of the sine and cosine functions is bounded by

-1

to estimate the maximum error.)

n>=

q,

\times

for

T_(n)

n>=

\times

for

M_(n)

Do the following with the given information.

\int_0^1 27cos(x^(2))dx

(a) Find the approximations

T_(8)

and

M_(8)

for the given integral. (Round your answer to six decimal places.)

T_(8)=,✓ Great work. M_(8)=,✓ Great jobt

(b) Estimate the errors in the approximations

T_(8)

and

M_(8)

in part (a). (Use the fact that the range of the sine and cosine functions is bounded by

!=1

to estimate the maximum error. Round your answer to seven decimal places.)

|E_(T)|<= |E_(M)|<=

q,

q,

(c) How large do we have to choose

n

so that the approximations

T_(n)

and

M_(n)

to the integral are accurate to within 0.0001 ? (Use the fact that the range of the sine and cosine functions is bounded by

-1

to estimate the maximum error.)

n>=

q,

\times

for

T_(n)

n>=

\times

for

M_(n)


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